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Efficient absorbing boundary conditions for conservation laws: Application to the piston problem of gas dynamics (2405.11588v1)

Published 19 May 2024 in math.NA and cs.NA

Abstract: In this work, we address the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to unphysical reflections. We investigate and implement some classes of relaxation methods and far-field operators to deal with this problem without significantly increasing the size of the computational domain. Relations are established between these techniques, and extensions of them are explored. In particular, we introduce a simple and robust relaxation method with a matrix-valued weight function that selectively absorbs outgoing waves. As a challenging model problem, we consider the Lagrangian formulation of the Euler equations for an isotropic gas with inflow boundary conditions determined by an oscillating piston.

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References (41)
  1. A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems. Journal of Computational Physics, 228(11):4200–4217, 2009.
  2. A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions. SIAM Journal on Scientific Computing, 24(3):955–978, 2003.
  3. Performance of different techniques of generation and absorption of free-surface waves in Computational Fluid Dynamics. Ocean Engineering, 214:107575, 2020.
  4. Nodal DG-FEM solution of high-order Boussinesq-type equations. Journal of Engineering Mathematics, 56(3):351–370, 2006.
  5. Allan Peter Engsig-Karup. Unstructured Nodal DG-FEM Solution of High-order Boussinesq-type Equations. PhD thesis, Technical University of Denmark, 2007.
  6. An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes. Journal of Computational Physics, 394:385–416, 2019.
  7. Central Schemes and Second Order Boundary Conditions for 1D Interface and Piston Problems in Lagrangian Coordinates. Commun. Comput. Phys, 8:797–822, 2010.
  8. Michael Giles. Non-reflecting boundary conditions for the Euler equations. Computational Fluid Dynamics Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 1988.
  9. John Goodrich. A Comparison of Three PML Treatments for CAA (and CFD). In 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference), Vancouver, British Columbia, Canada, 2008. American Institute of Aeronautics and Astronautics.
  10. High Order Strong Stability Preserving Time Discretizations. Journal of Scientific Computing, 38(3):251–289, 2009.
  11. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws. SIAM Review, 25(1):35–61, 1983. Publisher: Society for Industrial and Applied Mathematics.
  12. G. W Hedstrom. Nonreflecting boundary conditions for nonlinear hyperbolic systems. Journal of Computational Physics, 30(2):222–237, 1979.
  13. Fang Q. Hu. Absorbing Boundary Conditions. International Journal of Computational Fluid Dynamics, 18(6):513–522, 2004. Publisher: Taylor & Francis _eprint: https://doi.org/10.1080/10618560410001673524.
  14. Numerical simulations using conserved wave absorption applied to Navier–Stokes equation model. Coastal Engineering, 99:15–25, 2015.
  15. Propagation of strongly nonlinear plane waves. The Journal of the Acoustical Society of America, 94(3):1632–1642, 1993.
  16. Approximation of radiation boundary conditions. Journal of Computational Physics, 41(1):115–135, 1981.
  17. A wave generation toolbox for the open-source CFD library: OpenFoam®. International Journal for Numerical Methods in Fluids, 70(9):1073–1088, 2012. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.2726.
  18. Smadar Karni. Accelerated convergence to steady state by gradual far-field damping. AIAA Journal, 30(5):1220–1227, 1992.
  19. Smadar Karni. Far-Field Filtering Operators for Suppression of Reflection From Artificial Boundaries. SIAM Journal on Numerical Analysis, 33(3):1014–1047, 1996. Publisher: Society for Industrial and Applied Mathematics.
  20. WENOCLAW: A Higher Order Wave Propagation Method. In Sylvie Benzoni-Gavage and Denis Serre, editors, Hyperbolic Problems: Theory, Numerics, Applications, pages 609–616, Berlin, Heidelberg, 2008. Springer.
  21. PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems. SIAM Journal on Scientific Computing, 34(4):C210–C231, 2012.
  22. High-Order Wave Propagation Algorithms for Hyperbolic Systems. SIAM Journal on Scientific Computing, 35(1):A351–A377, 2013.
  23. R. Kosloff and D. Kosloff. Absorbing boundaries for wave propagation problems. Journal of Computational Physics, 63(2):363–376, 1986.
  24. Ideal fluids. In Fluid Mechanics, pages 1–43. Elsevier, 1987.
  25. Open boundaries in short wave simulations — A new approach. Coastal Engineering, 7(3):285–297, 1983.
  26. Philippe LeFloch. Shock Waves for Nonlinear Hyperbolic Systems in Nonconservative Form. 1989. http://conservancy.umn.edu/handle/11299/5107.
  27. Philippe G. LeFloch. Hyperbolic systems of conservation laws: the theory of classical and nonclassical shock waves. Lectures in mathematics ETH Zürich. Birkhäuser Verlag, Basel ; Boston, 2002.
  28. Boussinesq-Type Formulations for Fully Nonlinear and Extremely Dispersive Water Waves: Derivation and Analysis. Proceedings: Mathematical, Physical and Engineering Sciences, 459(2033):1075–1104, 2003. Publisher: The Royal Society.
  29. Clawpack: building an open source ecosystem for solving hyperbolic PDEs. PeerJ Computer Science, 2:e68, 2016. Publisher: PeerJ Inc.
  30. A fractional step method for unsteady free-surface flow with applications to non-linear wave dynamics. International Journal for Numerical Methods in Fluids, 28(2):293–315, 1998.
  31. Carlos Muñoz-Moncayo. Reproducibility repository for the paper: ”Efficient absorbing boundary conditions for conservation laws: Application to the piston problem of gas dynamics”. https://doi.org/10.5281/zenodo.11214432.(v1.0.0). Zenodo, 2024.
  32. Costas J. Papachristou. Aspects of Integrability of Differential Systems and Fields: A Mathematical Primer for Physicists. SpringerBriefs in Physics. Springer International Publishing, Cham, 2019.
  33. Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation. Journal of Scientific Computing, 25(1):129–155, 2005.
  34. R. Perić and M. Abdel-Maksoud. Reliable damping of free-surface waves in numerical simulations. Ship Technology Research, 63(1):1–13, 2016. Publisher: Taylor & Francis.
  35. Duyen Phan Thi My. Finite volume method for one-dimensional Euler equations and application to multi-fluid problem. PhD Thesis, Gran Sasso Science Institute, 2021.
  36. Sopheak Seng. Slamming And Whipping Analysis Of Ships. DCAMM Special Report. DTU Mechanical Engineering, 2012.
  37. Joel Smoller. Shock Waves and Reaction—Diffusion Equations, volume 258 of Grundlehren der mathematischen Wissenschaften. Springer, New York, NY, 1994.
  38. Eleuterio F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer, Berlin, Heidelberg, 2009.
  39. Simulation techniques for spatially evolving instabilities in compressible flow over a flat plate. Computers & Fluids, 26(7):713–739, 1997.
  40. Finite‐amplitude saturation of plane sound waves in air. The Journal of the Acoustical Society of America, 62(3):518–523, 1977.
  41. G. B. Whitham. Linear and nonlinear waves. Pure and applied mathematics. Wiley, New York, 1974.

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