Open Access
Volume 55, Number 3, May-June 2021
Page(s) 1199 - 1237
Published online 08 June 2021
  1. D.N. Arnold and R.S. Falk, A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal. 26 (1989) 1276–1290. [CrossRef] [MathSciNet] [Google Scholar]
  2. W. Barsukow, P.V.F. Edelmann, C. Klingenberg, F. Miczek and F.K. Röpke, A numerical scheme for the compressible low-Mach number regime of ideal fluid dynamics. J. Sci. Comput. 72 (2017) 623–646. [CrossRef] [Google Scholar]
  3. W. Barsukow, P.V.F. Edelmann, C. Klingenberg and F.K. Röpke, A low Mach Roe-type solver for the Euler equations allowing for gravity source terms. ESAIM: Proc. Surv. 58 (2017) 27–39. [Google Scholar]
  4. J. Bear and Y. Bachmat, Introduction to Modeling of Transport Phenomena in Porous Media. Springer Science & Business Media 4 (2012). [Google Scholar]
  5. P. Bruel, S. Delmas, J. Jung and V. Perrier, A low Mach correction able to deal with low Mach acoustics. J. Comput. Phys. 378 (2019) 723–759. [Google Scholar]
  6. T. Buffard, T. Gallouët and J.-M. Hérard, A sequel to a rough Godunov scheme: application to real gases. Comput. Fluids 29 (2000) 813–847. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Chalons, M. Girardin and S. Kokh, An all-regime Lagrange-Projection like scheme for the gas dynamics equations on unstructured meshes. Commun. Comput. Phys. 20 (2016) 188–233. [Google Scholar]
  8. S. Clain and D. Rochette, First-and second-order finite volume methods for the one-dimensional nonconservative Euler system. J. Comput. Phys. 228 (2009) 8214–8248. [Google Scholar]
  9. P. Colella and K. Pao, A projection method for low speed flows. J. Comput. Phys. 149 (1999) 245–269. [CrossRef] [Google Scholar]
  10. D.H. Cuong and M.D. Thanh, A Godunov-type scheme for the isentropic model of a fluid flow in a nozzle with variable cross-section. Appl. Math. Comput. 256 (2015) 602–629. [Google Scholar]
  11. G. Dal Maso, P.G. Lefloch and F. Murat, Definition and weak stability of nonconservative products. Journal de mathématiques pures et appliquées 74 (1995) 483–548. [Google Scholar]
  12. P. Degond and M. Tang, All speed scheme for the low Mach number limit of the isentropic Euler equations. Commun. Comput. Phys. 10 (2011) 1–31. [Google Scholar]
  13. S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number. J. Comput. Phys. 4 (2010) 978–1016. [Google Scholar]
  14. S. Dellacherie, P. Omnes and F. Rieper, The influence of cell geometry on the Godunov scheme applied to the linear wave equation. J. Comput. Phys. 229 (2010) 5315–5338. [Google Scholar]
  15. S. Dellacherie, J. Jung and P. Omnes, Preliminary results for the study of the Godunov scheme applied to the linear wave equation with porosity at low Mach number. ESAIM: Proc. Surv. 52 (2015) 105–126. [Google Scholar]
  16. S. Dellacherie, J. Jung, P. Omnes and P.-A. Raviart, Construction of modified Godunov type schemes accurate at any Mach number for the compressible Euler system. Math. Models Methods Appl. Sci. 26 (2016) 2525–2615. [CrossRef] [Google Scholar]
  17. T. Gallouet and J.M. Masella, Un schéma de Godunov approché. Comptes rendus de l’Academie des sciences Paris Serie 1 323 (1996) 77–84. [Google Scholar]
  18. T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. Fluids 32 (2003) 479–513. [CrossRef] [MathSciNet] [Google Scholar]
  19. C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int. J. Numer. Methods Eng. 79 (2009) 1309–1331. [Google Scholar]
  20. L. Gosse, A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11 (2001) 339–365. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.M. Greenberg and A.-Y. LeRoux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  22. H. Guillard, On the behavior of upwind schemes in the low Mach number limit. IV: P0 approximation on triangular and tetrahedral cells. Comput. Fluids 38 (2009) 1969–1972. [Google Scholar]
  23. H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63–86. [Google Scholar]
  24. D. Iampietro, F. Daude, P. Galon and J.-M. Hérard, A Mach-sensitive splitting approach for Euler-like systems. ESAIM: M2AN 52 (2018) 207–253. [EDP Sciences] [Google Scholar]
  25. S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Commun. Pure Appl. Math. 34 (1981) 481–524. [Google Scholar]
  26. D. Kröner and M.D. Thanh, Numerical solutions to compressible flows in a nozzle with variable cross-section. SIAM J. Numer. Anal. 43 (2005) 796–824. [Google Scholar]
  27. P.G. Lefloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Commun. Math. Sci. 1 (2003) 763–797. [CrossRef] [MathSciNet] [Google Scholar]
  28. X.-S. Li and C.-W. Gu, An all-speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour. J. Comput. Phys. 227 (2008) 5144–5159. [CrossRef] [Google Scholar]
  29. X.-S. Li, C.-W. Gu and J.-Z. Xu, Development of Roe-type scheme for all-speed flows based on preconditioning method. Comput. Fluids 38 (2009) 810–817. [Google Scholar]
  30. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer Science & Business Media 53 (2012). [Google Scholar]
  31. R.A. Nicolaides, Analysis and convergence of the MAC scheme. I: The linear problem. SIAM J. Numer. Anal. 29 (1992) 1579–1591. [CrossRef] [MathSciNet] [Google Scholar]
  32. R.A. Nicolaides, Direct discretization of planar div-curl problems. SIAM J. Numer. Anal. 29 (1992) 32–56. [CrossRef] [MathSciNet] [Google Scholar]
  33. K. Oßwald, A. Siegmund, P. Birken, V. Hannemann and A. Meister, L2 Roe: a low dissipation version of Roe’s approximate Riemann solver for low Mach numbers. Int. J. Numer. Methods Fluids 81 (2016) 71–86. [Google Scholar]
  34. M. Pelanti, Low Mach number preconditioning techniques for Roe-type and HLLC-type methods for a two-phase compressible flow model. Appl. Math. Comput. 310 (2017) 112–133. [Google Scholar]
  35. M. Pelanti and K.-M. Shyue, A Roe-type scheme with low Mach number preconditioning for a two-phase compressible flow model with pressure relaxation. Bull. Braz. Math. Soc. New Ser. 47 (2016) 655–669. [Google Scholar]
  36. F. Rieper, On the dissipation mechanism of upwind-schemes in the low Mach number regime: a comparison between Roe and HLL. J. Comput. Phys. 229 (2010) 221–232. [Google Scholar]
  37. F. Rieper, A low-Mach number fix for Roe’s approximate Riemann solver. J. Comput. Phys. 230 (2011) 5263–5287. [Google Scholar]
  38. F. Rieper and G. Bader, The influence of cell geometry on the accuracy of upwind schemes in the low Mach number regime. J. Comput. Phys. 228 (2009) 2918–2933. [Google Scholar]
  39. D. Rochette and S. Clain, Two-dimensional computation of gas flow in a porous bed characterized by a porosity jump. J. Comput. Phys. 219 (2006) 104–119. [Google Scholar]
  40. D. Rochette, S. Clain and T. Buffard, Numerical scheme to complete a compressible gas flow in variable porosity media. Int. J. Comput. Fluid Dyn. 19 (2005) 299–309. [Google Scholar]
  41. D. Rochette, S. Clain and F. Gentils, Numerical investigations on the pressure wave absorption and the gas cooling interacting in a porous filter, during an internal arc fault in a medium-voltage cell. IEEE Trans. Power Delivery 23 (2007) 203–212. [Google Scholar]
  42. S. Schochet, Fast singular limits of hyperbolic PDEs. J. Differ. Equ. 114 (1994) 476–512. [Google Scholar]
  43. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Springer (1998) 325–432. [Google Scholar]
  44. S.C. Spiegel, H.T. Huynh and J.R. DeBonis, A survey of the isentropic Euler vortex problem using high-order methods. In: 22nd AIAA Computational Fluid Dynamics Conference. AIAA paper 2015-2444 (2015). [Google Scholar]
  45. A. Thomann, G. Puppo and C. Klingenberg, An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity. J. Comput. Phys. 420 (2020) 109723. [Google Scholar]
  46. E. Turkel, Preconditioning techniques in computational fluid dynamics. Ann. Rev. Fluid Mech. 31 (1999) 385–416. [NASA ADS] [CrossRef] [Google Scholar]

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