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All issues Volume 56 / No 1 (January-February 2022) ESAIM: M2AN, 56 1 (2022) 317-347 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 1, January-February 2022
Page(s) 317 - 347
DOI https://doi.org/10.1051/m2an/2021087
Published online 10 February 2022
  1. R. Abgrall, A genuinely multidimensional Riemann solver. hal:inria-00074814 (1993). [Google Scholar]
  2. D. Amadori and L. Gosse, Error Estimates for Well-Balanced Schemes on Simple Balance Laws: One-Dimensional Position-Dependent Models. BCAM Springer Briefs in Mathematics. Springer (2015). [CrossRef] [Google Scholar]
  3. D.S. Balsara, A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and magnetohydrodynamic flows. J. Comput. Phys. 231 (2012) 7476–7503. [CrossRef] [MathSciNet] [Google Scholar]
  4. W. Barsukow, Stationarity and vorticity preservation for the linearized Euler equations in multiple spatial dimensions. In: International Conference on Finite Volumes for Complex Applications. Springer (2017) 449–456. [Google Scholar]
  5. W. Barsukow, Stationarity preserving schemes for multi-dimensional linear systems. Math. Comput. 88 (2019) 1621–1645. [Google Scholar]
  6. 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. [Google Scholar]
  7. M. Brio, A.R. Zakharian and G.M. Webb, Two-dimensional Riemann solver for Euler equations of gas dynamics. J. Comput. Phys. 167 (2001) 177–195. [CrossRef] [Google Scholar]
  8. C. Chalons, M. Girardin and S. Kokh, Large time step and asymptotic preserving numerical schemes for the gas dynamics equations with source terms. SIAM J. Sci. Comput. 35 (2013) A2874–A2902. [CrossRef] [Google Scholar]
  9. R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations. Interscience, New York (1962). [Google Scholar]
  10. P. Colella, Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 171–200. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number. J. Comput. Phys. 229 (2010) 978–1016. [Google Scholar]
  12. 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]
  13. L.C. Evans, Partial differential equations. Graduate Stud. Math. 19 (1998) 7. [Google Scholar]
  14. T.A. Eymann and P.L. Roe, Multidimensional active flux schemes. In: 21st AIAA Computational Fluid Dynamics Conference (2013). [Google Scholar]
  15. M. Fey, Multidimensional upwinding. Part I. The method of transport for solving the Euler equations. J. Comput. Phys. 143 (1998) 159–180. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Fey, Multidimensional upwinding. Part II. Decomposition of the Euler equations into advection equations. J. Comput. Phys. 143 (1998) 181–199. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Franck and L. Gosse, Stability of a Kirchhoff-Roe scheme for two-dimensional linearized Euler systems. Annali dell’Universita’ di Ferrara 64 (2018) 335–360. [CrossRef] [MathSciNet] [Google Scholar]
  18. I.M. Gelfand and G.E. Shilov, Generalized Functions. Vol. 1. Properties and Operations. Translated from the Russian by Eugene Saletan (1964). [Google Scholar]
  19. H. Gilquin, J. Laurens and C. Rosier, Multi-dimensional Riemann problems for linear hyperbolic systems: part II. In: Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, Springer (1993) 284–290. [CrossRef] [Google Scholar]
  20. H. Gilquin, J. Laurens and C. Rosier, Multi-dimensional Riemann problems for linear hyperbolic systems. ESAIM: M2AN 30 (1996) 527–548. [CrossRef] [EDP Sciences] [Google Scholar]
  21. E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Vol 118. Springer Science & Business Media (2013). [Google Scholar]
  22. S.K. Godunov, Vospominaniya o raznostnyh shemah: doklad na mezhdunarodnom simpoziume “Metod Godunova v gazovoy dinamike” Michigan 1997. Nauchnaya Kniga (1997). [Google Scholar]
  23. S.K. Godunov, Reminiscences about numerical schemes. Jou. Preprint arXiv:0810.0649 (2008). [Google Scholar]
  24. S.K. Godunov, A.V. Zabrodin, M.I. Ivanov, A.N. Kraiko and G.P. Prokopov, Numerical Solution of Multidimensional Problems of Gas Dynamics. Vol. 1. Moscow Izdatel Nauka (1976). [Google Scholar]
  25. H. Guillard and A. Murrone, On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes. Comput. Fluids 33 (2004) 655–675. [Google Scholar]
  26. 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]
  27. L. Hörmander, Linear Partial Differential Operators. Vol. 116. Springer (2013). [Google Scholar]
  28. F. John, Partial differential equations. Appl. Math. Sci. 1 (1978) 198. [Google Scholar]
  29. F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations. Springer-Verlag, Berlin-Heidelberg-New York (1981). [CrossRef] [Google Scholar]
  30. 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]
  31. R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: one-dimensional flow. J. Comput. Phys. 121 (1995) 213–237. [Google Scholar]
  32. R.J. LeVeque, Wave propagation algorithms for multidimensional hyperbolic systems. J. Comput. Phys. 131 (1997) 327–353. [CrossRef] [Google Scholar]
  33. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Vol. 31. Cambridge University Press (2002). [CrossRef] [Google Scholar]
  34. X.-S. Li and C.-W. Gu, Mechanism of Roe-type schemes for all-speed flows and its application. Comput. Fluids 86 (2013) 56–70. [CrossRef] [MathSciNet] [Google Scholar]
  35. T. Li and W. Sheng, The general Riemann problem for the linearized system of two-dimensional isentropic flow in gas dynamics. J. Math. Anal. App. 276 (2002) 598–610. [CrossRef] [Google Scholar]
  36. J. Li, M. Lukacova-Medvidova and G. Warnecke, Evolution Galerkin schemes applied to two-dimensional Riemann problems for the wave equation system. Dyn. Syst. 9 (2003) 559–576. [Google Scholar]
  37. M. Lukacova-Medvidova, K. Morton and G. Warnecke, Evolution Galerkin methods for hyperbolic systems in two space dimensions. Math. Comput. Am. Math. Soc. 69 (2000) 1355–1384. [CrossRef] [Google Scholar]
  38. M. Lukacova-Medvidova, K.W. Morton and G. Warnecke, Finite volume evolution Galerkin methods for hyperbolic systems. SIAM J. Sci. Comput. 26 (2004) 1–30. [CrossRef] [MathSciNet] [Google Scholar]
  39. M. Lukacova-Medvidova, J. Saibertova, G. Warnecke and Y. Zahaykah, On evolution Galerkin methods for the Maxwell and the linearized Euler equations. App. Math. 49 (2004) 415–439. [CrossRef] [Google Scholar]
  40. G. Métivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal. 158 (2001) 61–90. [CrossRef] [MathSciNet] [Google Scholar]
  41. K.W. Morton and P.L. Roe, Vorticity-preserving Lax–Wendroff-type schemes for the system wave equation. SIAM J. Sci. Comput. 23 (2001) 170–192. [CrossRef] [MathSciNet] [Google Scholar]
  42. 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]
  43. B. O’Neill, Semi-Riemannian Geometry With Applications to Relativity. Vol 103. Academic Press (1983). [Google Scholar]
  44. S. Ostkamp, Multidimensional characteristic Galerkin methods for hyperbolic systems. Math. Methods Appl. Sci. 20 (1997) 1111–1125. [CrossRef] [MathSciNet] [Google Scholar]
  45. J. Rauch, Partial differential equations. In: Vol. 128 of Graduate Texts in Mathematics (1991). [CrossRef] [Google Scholar]
  46. P. Roe, Is discontinuous reconstruction really a good idea? J. Sci. Comput. 73 (2017) 1094–1114. [CrossRef] [MathSciNet] [Google Scholar]
  47. P. Roe, Multidimensional upwinding. Handb. Numer. Anal. 18 (2017) 53–80. [Google Scholar]
  48. W. Rudin, Functional Analysis. International Series in Pure and Applied Mathematics. MacGraw Hill Inc., New York (1991). [Google Scholar]
  49. L. Schwartz, Théorie des distributions. Hermann Paris (1978). [Google Scholar]
  50. M.E. Taylor, Partial Differential Equations. I. Basic Theory. Springer (1996). [Google Scholar]
  51. B.J.R. Thornber and D. Drikakis, Numerical dissipation of upwind schemes in low Mach flow. Int. J. Numer. Methods Fluids 56 (2008) 1535–1541. [CrossRef] [Google Scholar]
  52. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer Science & Business Media (2009). [Google Scholar]
  53. Y. Zheng, Systems of Conservation Laws: Two-Dimensional Riemann Problems. Springer Science & Business Media (2001). [CrossRef] [Google Scholar]
  54. C. Zuily, Éléments de distributions et d’équations aux dérivées partielles: cours et problèmes résolus. Vol 130. Dunod (2002). [Google Scholar]

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