Free Access
Volume 39, Number 4, July-August 2005
Page(s) 649 - 692
Published online 15 August 2005
  1. R. Abgrall and S. Karni, Computations of compressible multifluids. J. Comput. Phys. 169 (2001) 594–623. [CrossRef] [MathSciNet]
  2. J.J. Adimurthi and G.D. Veerappa Gowda, Godunov-type methods for conservation laws with a flux function discontinuous in space. SIAM J. Numer. Anal. 42 (2004) 179–208. [CrossRef] [MathSciNet]
  3. E. Audusse and B. Perthame, Uniqueness for a scalar conservation law with discontinuous flux via adapted entropies, Inria research report No. 5261 (2004), France.
  4. D. Bale, R. LeVeque, S. Mitran and J. Rossmanith, A wave propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM J. Sci. Comput. 24 (2002) 955–978. [CrossRef] [MathSciNet]
  5. T. Barberon, Modélisation mathématique et numérique de la cavitation dans les écoulements multiphasiques compressibles. Thesis, University of Toulon, France (2002).
  6. F. Coquel, E. Godlewski, P.-A. Raviart et al., Numerical coupling of models in the context of fluid flows, work in preparation.
  7. S. Cordier, Hyperbolicity of the hydrodynamic model of plasmas under the quasi-neutrality hypothesis. Math. Methods Appl. Sci. 18 (1995) 627–647. [CrossRef] [MathSciNet]
  8. B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition. Numer. Math. 89 (2001) 99–134. [CrossRef] [MathSciNet]
  9. S. Diehl, On scalar conservation laws with point source and discontinuous flux function. SIAM J. Numer. Anal. 26 (1995) 1425–1451.
  10. F. Dubois and P. Le Floch, Boundary conditions for nonlinear hyperbolic systems of conservation laws. J. Differential Equations 71 (1988) 93–122. [CrossRef] [MathSciNet]
  11. R. Fedkiw, T. Aslam, B. Merriman and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152 (1999) 457–492. [CrossRef] [MathSciNet]
  12. G. Gallice, Positive and entropy stable Godunov-type schemes for gas dynamics and MHD equations in Lagrangian or Eulerian coordinates. Numer. Math. 94 (2003) 673–713. [MathSciNet]
  13. M. Gisclon, Étude des conditions aux limites pour un système strictement hyperbolique via l'approximation parabolique. J. Math. Pures Appl. 75 (1996) 485–508. [MathSciNet]
  14. M. Gisclon and D. Serre, Étude des conditions aux limites pour un système hyperbolique, via l'approximation parabolique. C. R. Acad. Sci. Paris, Série I 319 (1994) 377–382.
  15. M. Gisclon and D. Serre, Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov. RAIRO Modél. Math. Anal. Numér. 31 (1997) 359–380. [MathSciNet]
  16. E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Appl. Math. Sci. 118, Springer, New York (1996).
  17. E. Godlewski and P.-A. Raviart, The numerical coupling of nonlinear hyperbolic systems of conservation laws: I. The scalar case. Numer. Math. 97 (2004) 81–130. [CrossRef] [MathSciNet]
  18. M. Göz and C.-D. Munz, Approximate Riemann solvers for fluid flow with material interfaces. Numerical methods for wave propagation (Manchester, 1995), Kluwer Acad. Publ., Dordrecht. Fluid Mech. Appl. 47 (1998) 211–235.
  19. J.M. Greenberg, A.Y. Leroux, R. Baraille and A. Noussair, Analysis and approximation of conservation laws with source terms. SIAM J. Numer. Anal. 34 (1997) 1980–2007. [CrossRef] [MathSciNet]
  20. A. Harten, P.D. Lax and B. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35–61. [CrossRef] [MathSciNet]
  21. E. Isaacson and B. Temple, Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52 (1992) 1260–1278. [CrossRef] [MathSciNet]
  22. K. Karlsen, N. Risebro and J. Towers, Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. IMA J. Numer. Anal. 22 (2002) 623–664. [CrossRef] [MathSciNet]
  23. R. Klausen and N. Risebro, Stability of conservation laws with discontinuous coefficients. J. Differential Equations 157 (1999) 41–60. [CrossRef] [MathSciNet]
  24. C. Klingenberg and N.H. Risebro, Stability of a resonant system of conservation laws modeling polymer flow with gravitation, J. Differential Equations 170 (2001) 344–380.
  25. S. Kokh, Aspects numériques et théoriques de la modélisation des écoulements diphasiques compressibles par des méthodes de capture d'interface. Thesis, University Paris 6, France (2001).
  26. K.-C. Le Thanh and P.-A. Raviart, Un modèle de plasma partiellement ionisé. Rapport CEA-R-6036, France (2003).
  27. W.K. Lyons, Conservation laws with sharp inhomogeneities. Quart. Appl. Math. 40 (1983) 385–393.
  28. S. Mishra, Convergence of upwind finite difference schemes for a scalar conservation law with indefinite discontinuities in the flux function. Ntnu Preprints on Conservation Laws 2003-077 (2003).
  29. C.-D. Munz, On Godunov-type schemes for Lagrangian gas dynamics. SIAM J. Numer. Anal. (1994), 17–42.
  30. T. Pougeard Dulimbert, Extraction de faisceaux d'ions à partir de plasmas neutres: Modélisation et simulation numérique. Thesis, University Paris 6, France (2001).
  31. N. Seguin and J. Vovelle, Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. Math. Models Methods Appl. Sci. 13 (2003) 221–257. [CrossRef] [MathSciNet] [PubMed]
  32. D. Serre, Systèmes de lois de conservation I and II. Diderot éditeur, Paris (1996).
  33. J. Towers, A difference scheme for conservation laws with a discontinuous flux: the nonconvex case. SIAM J. Numer. Anal. 39 (2001) 1197–1218. [CrossRef] [MathSciNet]
  34. Y.B. Zel'dovich and Y.P. Raizer, Physics of shock waves and high-temperature hydrodynamic phenomena, Vol. II. Academic Press (1967).

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