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A generalized formulation for gradient schemes in unstructured finite volume method
Published 9 Feb 2024 in math.NA, cs.NA, math-ph, math.MP, and physics.flu-dyn | (2402.06199v1)
Abstract: We present a generic framework for gradient reconstruction schemes on unstructured meshes using the notion of a dyadic sum-vector product. The proposed formulation reconstructs centroidal gradients of a scalar from its directional derivatives along specific directions in a suitably defined neighbourhood. We show that existing gradient reconstruction schemes can be encompassed within this framework by a suitable choice of the geometric vectors that define the dyadic sum tensor. The proposed framework also allows us to re-interpret certain hybrid schemes, which might not be derivable through traditional routes. Additionally, a generalization of flexible gradient schemes is proposed that can be employed to enhance the robustness of consistent gradient schemes without compromising on the accuracy of the computed gradients.
- Moukalled, F., Mangani, L., Darwish, M., et al.: The Finite Volume Method in Computational Fluid Dynamics. Springer, New York (2016) Mavriplis [2003] Mavriplis, D.: Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. In: 16th AIAA Computational Fluid Dynamics Conference, p. 3986 (2003) Shima et al. [2013] Shima, E., Kitamura, K., Haga, T.: Green–gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA journal 51(11), 2740–2747 (2013) Diskin and Thomas [2008] Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mavriplis, D.: Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. In: 16th AIAA Computational Fluid Dynamics Conference, p. 3986 (2003) Shima et al. [2013] Shima, E., Kitamura, K., Haga, T.: Green–gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA journal 51(11), 2740–2747 (2013) Diskin and Thomas [2008] Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Shima, E., Kitamura, K., Haga, T.: Green–gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA journal 51(11), 2740–2747 (2013) Diskin and Thomas [2008] Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Mavriplis, D.: Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. In: 16th AIAA Computational Fluid Dynamics Conference, p. 3986 (2003) Shima et al. [2013] Shima, E., Kitamura, K., Haga, T.: Green–gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA journal 51(11), 2740–2747 (2013) Diskin and Thomas [2008] Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Shima, E., Kitamura, K., Haga, T.: Green–gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA journal 51(11), 2740–2747 (2013) Diskin and Thomas [2008] Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Shima, E., Kitamura, K., Haga, T.: Green–gauss/weighted-least-squares hybrid gradient reconstruction for arbitrary polyhedra unstructured grids. AIAA journal 51(11), 2740–2747 (2013) Diskin and Thomas [2008] Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Diskin, B., Thomas, J.: Accuracy of gradient reconstruction on grids with high aspect ratio. NIA report 12, 2008 (2008) Wang et al. [2017] Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Wang, Q., Ren, Y.-X., Pan, J., Li, W.: Compact high order finite volume method on unstructured grids iii: Variational reconstruction. Journal of Computational physics 337, 1–26 (2017) Nishikawa [2018] Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Nishikawa, H.: From hyperbolic diffusion scheme to gradient method: Implicit green–gauss gradients for unstructured grids. Journal of Computational Physics 372, 126–160 (2018) Oxtoby et al. [2019] Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Oxtoby, O., Syrakos, A., Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A family of first-order accurate gradient schemes for finite volume methods (2019) Syrakos et al. [2023] Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Syrakos, A., Oxtoby, O., de Villiers, E., Varchanis, S., Dimakopoulos, Y., Tsamopoulos, J.: A unification of least-squares and green–gauss gradients under a common projection-based gradient reconstruction framework. Mathematics and Computers in Simulation 205, 108–141 (2023) https://doi.org/10.1016/j.matcom.2022.09.008 Deka et al. [2018] Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Deka, M., Brahmachary, S., Thirumalaisamy, R., Dalal, A., Natarajan, G.: A new green–gauss reconstruction on unstructured meshes. part i: Gradient reconstruction. Journal of Computational Physics (2018) Feng [2020] Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Feng, X.: Cell-centered finite volume methods. In: Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, pp. 125–337. Springer, ??? (2020) Deka et al. [2023] Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Deka, M., Assam, A., Natarajan, G.: A least squares perspective of green–gauss gradient schemes. Physics of Fluids 35(3) (2023) Nishikawa [2021] Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Nishikawa, H.: A flexible gradient method for unstructured-grid solvers. International Journal for Numerical Methods in Fluids 93(6), 2015–2021 (2021) Sozer et al. [2014] Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Sozer, E., Brehm, C., Kiris, C.C.: Gradient calculation methods on arbitrary polyhedral unstructured meshes for cell-centered cfd solvers. In: 52nd Aerospace Sciences Meeting, p. 1440 (2014) Syrakos et al. [2017] Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Syrakos, A., Varchanis, S., Dimakopoulos, Y., Goulas, A., Tsamopoulos, J.: A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Physics of Fluids 29(12), 127103 (2017) Diskin and Thomas [2011] Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Diskin, B., Thomas, J.L.: Comparison of node-centered and cell-centered unstructured finite-volume discretizations: inviscid fluxes. AIAA journal 49(4), 836–854 (2011) Jasak [1996] Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Jasak, H.: Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London) (1996) Mahesh et al. [2004] Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Mahesh, K., Constantinescu, G., Moin, P.: A numerical method for large-eddy simulation in complex geometries. Journal of Computational Physics 197(1), 215–240 (2004) Ghods and Herrmann [2013] Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Ghods, S., Herrmann, M.: A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods. Physica Scripta 2013(T155), 014050 (2013) Manik et al. [2018] Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Manik, J., Dalal, A., Natarajan, G.: A generic algorithm for three-dimensional multiphase flows on unstructured meshes. International Journal of Multiphase Flow 106, 228–242 (2018) Weller [2014] Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Weller, H.: Non-orthogonal version of the arbitrary polygonal c-grid and a new diamond grid. Geoscientific Model Development 7(3), 779–797 (2014) Aguerre et al. [2018] Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018) Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
- Aguerre, H.J., Pairetti, C.I., Venier, C.M., Damián, S.M., Nigro, N.M.: An oscillation-free flow solver based on flux reconstruction. Journal of Computational Physics 365, 135–148 (2018)
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