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A component-splitting implicit time integration for multicomponent reacting flows simulations (2403.03440v1)

Published 6 Mar 2024 in math.NA, cs.NA, and physics.comp-ph

Abstract: A component-splitting method is proposed to improve convergence characteristics for implicit time integration of compressible multicomponent reactive flows. The characteristic decomposition of flux jacobian of multicomponent Navier-Stokes equations yields a large sparse eigensystem, presenting challenges of slow convergence and high computational costs for implicit methods. To addresses this issue, the component-splitting method segregates the implicit operator into two parts: one for the flow equations (density/momentum/energy) and the other for the component equations. Each part's implicit operator employs flux-vector splitting based on their respective spectral radii to achieve accelerated convergence. This approach improves the computational efficiency of implicit iteration, mitigating the quadratic increase in time cost with the number of species. Two consistence corrections are developed to reduce the introduced component-splitting error and ensure the numerical consistency of mass fraction. Importantly, the impact of component-splitting method on accuracy is minimal as the residual approaches convergence. The accuracy, efficiency, and robustness of component-splitting method are thoroughly investigated and compared with the coupled implicit scheme through several numerical cases involving thermo-chemical nonequilibrium hypersonic flows. The results demonstrate that the component-splitting method decreases the required number of iteration steps for convergence of residual and wall heat flux, decreases the computation time per iteration step, and diminishes the residual to lower magnitude. The acceleration efficiency is enhanced with increases in CFL number and number of species.

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References (42)
  1. J. John D. Anderson, Hypersonic and high temperature gas dynamics, third edition (AIAA Education Series, 2019).
  2. C. Park, “Assessment of two-temperature kinetic model for ionizing air,” Journal of Thermophysics and Heat Transfer 3, 233–244 (1989).
  3. Z. Shen, W. Yan,  and G. Yuan, “A robust and contact resolving riemann solver on unstructured mesh, Part I, Euler method,” Journal of Computational Physics 268, 432–455 (2014).
  4. A. Jameson, “Numerical solution of the euler equations for compressible inviscid fluids,” Numerical methods for the Euler equations of Fluid Dynamics , 199–245 (1985).
  5. A. Jameson, “Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings,” in 10th computational fluid dynamics conference (1991) p. 1596.
  6. J. Blazek, Computational fluid dynamics: principles and applications, third edition ed. (Butterworth-Heinemann, 2015) pp. 176–181.
  7. U. M. Ascher, S. J. Ruuth,  and B. T. R. Wetton, “Implicit-explicit methods for time-dependent partial differential equations,” SIAM Journal on Numerical Analysis 32, 797–823 (1995).
  8. L. Li and D. Xu, “Alternating direction implicit-euler method for the two-dimensional fractional evolution equation,” Journal of Computational Physics 236, 157–168 (2013).
  9. U. M. Ascher, S. J. Ruuth,  and R. J. Spiteri, “Implicit-explicit runge-kutta methods for time-dependent partial differential equations,” Applied Numerical Mathematics 25, 151–167 (1997).
  10. P. Roe, “Approximate riemann solvers, parameter vectors, and difference schemes,” Journal of Computational Physics 135, 250–258 (1997).
  11. J. L. Steger and R. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,” Journal of Computational Physics 40, 263–293 (1981).
  12. R. Nichols, R. Tramel,  and P. Buning, “Solver and turbulence model upgrades to overflow 2 for unsteady and high-speed applications,” in 24th AIAA Applied Aerodynamics Conference (2006).
  13. W. Briley and H. McDonald, “Solution of the multidimensional compressible navier-stokes equations by a generalized implicit method,” Journal of Computational Physics 24, 372–397 (1977).
  14. Y. Saad and M. H. Schultz, “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing 7, 856–869 (1986).
  15. H. Lomax and J. L. Steger, “Relaxation methods in fluid mechanics,” Annual Review of Fluid Mechanics 7, 63–88 (1975).
  16. S. Yoon and A. Jameson, “Lower-upper symmetric-gauss-seidel method for the euler and navier-stokes equations,” AIAA Journal 26, 1025–1026 (1988a).
  17. R. M. Beam and R. Warming, “An implicit finite-difference algorithm for hyperbolic systems in conservation-law form,” Journal of Computational Physics 22, 87–110 (1976).
  18. D. Knoll and D. Keyes, “Jacobian-free newton-krylov methods: a survey of approaches and applications,” Journal of Computational Physics 193, 357–397 (2004).
  19. Y. Jin, F. Liao,  and J. Cai, “Convergence acceleration for subiterative DDADI/D3ADI using multiblock implicit boundary condition,” Journal of Computational Physics 429, 110009 (2021).
  20. R. Zhang, S. Liu, J. Chen, C. Zhuo,  and C. Zhong, “A conservative implicit scheme for three-dimensional steady flows of diatomic gases in all flow regimes using unstructured meshes in the physical and velocity spaces,” Physics of Fluids 36, 016114 (2024).
  21. B. Zhou, X. Huang, D. Bi, K. Zhang,  and M. Zhou, “Efficient same-dimensional implicit time advancement parallel scheme and optimization methods for the iteration parameters using a graphics-processing unit,” Physics of Fluids 34, 097122 (2022).
  22. W. Cao, Y. Liu, X. Shan, C. Gao,  and W. Zhang, “A novel convergence enhancement method based on online dimension reduction optimization,” Physics of Fluids 35, 036124 (2023).
  23. G. Strang, “On the construction and comparison of difference schemes,” SIAM Journal on Numerical Analysis 5, 506–517 (1968).
  24. H. Dong, F. Zhang, C. Xu,  and J. Liu, “An improved uncoupled finite volume solver for simulating unsteady shock-induced combustion,” Computers and Fluids 167, 146–157 (2018).
  25. M. A. Hansen and J. C. Sutherland, “Pseudotransient continuation for combustion simulation with detailed reaction mechanisms,” SIAM Journal on Scientific Computing 38, B272–B296 (2016).
  26. X. Chen and S. Fu, “Convergence acceleration for high-order shock-fitting methods in hypersonic flow applications with efficient implicit time-stepping schemes,” Computers and Fluids 210, 104668 (2020).
  27. H. Su, J. Cai, K. Qu,  and S. Pan, “Numerical simulations of inert and reactive highly underexpanded jets,” Physics of Fluids 32, 036104 (2020).
  28. P. J. Martínez Ferrer, R. Buttay, G. Lehnasch,  and A. Mura, “A detailed verification procedure for compressible reactive multicomponent navier-stokes solvers,” Computers and Fluids 89, 88–110 (2014).
  29. S. Yoon and A. Jameson, “Lower-upper symmetric-gauss-seidel method for the euler and navier-stokes equations,” AIAA Journal 26, 1025–1026 (1988b).
  30. R. Vicquelin, B. Fiorina, S. Payet, N. Darabiha,  and O. Gicquel, “Coupling tabulated chemistry with compressible cfd solvers,” Proceedings of the Combustion Institute 33, 1481–1488 (2011).
  31. X. Chen, L. Wang,  and S. Fu, “Secondary instability of the hypersonic high-enthalpy boundary layers with thermal–chemical nonequilibrium effects,” Physics of Fluids 33, 034132 (2021).
  32. S. Karl, J. M. Schramm,  and K. Hannemann, “High enthalpy cylinder flow in heg: A basis for cfd validation,” in 33rd AIAA Fluid Dynamics Conference and Exhibit (2003) p. 4252.
  33. P. A. Gnoffo, R. N. Gupta,  and J. L. Shinn, “Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium,” Tech. Rep. NASA-TP-2867 (Langley Research Center Hampton, 1989).
  34. B. Van Leer, “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method,” Journal of Computational Physics 32, 101–136 (1979).
  35. P. K. Sweby, “High resolution schemes using flux limiters for hyperbolic conservation laws,” SIAM Journal on Numerical Analysis 21, 995–1011 (1984).
  36. P. SPALART and S. ALLMARAS, “A one-equation turbulence model for aerodynamic flows,” in 30th Aerospace Sciences Meeting and Exhibit (1992) p. 439.
  37. D. Knight, J. Longo, D. Drikakis, D. Gaitonde, A. Lani, I. Nompelis, B. Reimann,  and L. Walpot, “Assessment of cfd capability for prediction of hypersonic shock interactions,” Progress in Aerospace Sciences 48-49, 8–26 (2012), assessment of Aerothermodynamic Flight Prediction Tools.
  38. N. Adhikari and A. A. Alexeenko, “A general form of Macheret–Fridman classical impulsive dissociation model for nonequilibrium flows,” Physics of Fluids 33, 056109 (2021).
  39. N. J. Georgiadis, C. L. Rumsey,  and G. P. Huang, “Revisiting turbulence model validation for high-mach number axisymmetric compression corner flows,” in 53rd AIAA Aerospace Sciences Meeting (2015) p. 0316.
  40. M. I. Kussoy and C. C. Horstman, “Documentation of two- and three-dimensional hypersonic shock wave/turbulent boundary layer interaction flows,” Tech. Rep. NASA-TM-101075 (NASA Ames Research Center, 1989).
  41. M. MacLean, E. Mundy, T. Wadhams, M. Holden,  and R. Parker, “Analysis and ground test of aerothermal effects on spherical capsule geometries,” in 38th Fluid Dynamics Conference and Exhibit (2008) p. 4273.
  42. J. Hao, J. Wang,  and C. Lee, “Numerical study of hypersonic flows over reentry configurations with different chemical nonequilibrium models,” Acta Astronautica 126, 1–10 (2016).
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