Free access
Issue
ESAIM: M2AN
Volume 44, Number 6, November-December 2010
Page(s) 1319 - 1348
DOI http://dx.doi.org/10.1051/m2an/2010033
Published online 10 May 2010
  1. A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutière, P.A. Raviart and N. Seguin, Working group on the interfacial coupling of models. http://www.ann.jussieu.fr/groupes/cea (2003).
  2. N. Andrianov and G. Warnecke, The Riemann problem for the Baer-Nunziato two-phase flow model. J. Comput. Phys. 195 (2004) 434–464. [CrossRef] [MathSciNet]
  3. E. Audusse, F. Bouchut, M.O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrodynamic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050–2065. [CrossRef] [MathSciNet]
  4. M.R. Baer and J.W. Nunziato, A two-phase mixture theory for the deflagration to detonation transition (DDT) in reactive granular materials. Int. J. Multiphase Flow 12 (1986) 861–889. [CrossRef]
  5. F. Bouchut, Nonlinear stability of Finite Volume methods for hyperbolic conservation laws, and well-balanced schemes for sources, Frontiers in Mathematics series. Birkhauser (2004).
  6. B. Boutin, F. Coquel and E. Godlewski, Dafermos Regularization for Interface Coupling of Conservation Laws, in Hyperbolic problems: Theory, Numerics, Applications, Springer (2008) 567–575.
  7. 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]
  8. A. Chinnayya, A.Y. Le Roux and N. Seguin, A well-balanced numerical scheme for shallow-water equations with topography: the resonance phenomena. Int. J. Finite Volumes 1 (2004) available at http://www.latp.univ-mrs.fr/IJFV/.
  9. F. Coquel, T. Gallouët, J.M. Hérard and N. Seguin, Closure laws for a two-fluid two-pressure model. C. R. Acad. Sci. Paris. I-332 (2002) 927–932.
  10. R. Eymard, T. Gallouët and R. Herbin, Finite Volume methods, in Handbook of Numerical Analysis VII, P.G. Ciarlet and J.L. Lions Eds., North Holland (2000) 715–1022.
  11. T. Gallouët, J.-M. Hérard and N. Seguin, A hybrid scheme to compute contact discontinuities in one dimensional Euler systems. ESAIM: M2AN 36 (2002) 1133–1159. [CrossRef] [EDP Sciences]
  12. T. Gallouët, J.-M. Hérard and N. Seguin, Some recent Finite Volume schemes to compute Euler equations using real gas EOS. Int. J. Num. Meth. Fluids 39 (2002) 1073–1138. [CrossRef]
  13. 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]
  14. T. Gallouët, J.-M. Hérard and N. Seguin, Numerical modelling of two phase flows using the two-fluid two-pressure approach. Math. Mod. Meth. Appl. Sci. 14 (2004) 663–700. [CrossRef] [MathSciNet]
  15. L. Girault and J.-M. Hérard, Multidimensional computations of a two-fluid hyperbolic model in a porous medium. AIAA paper 2009–3540 (2009) available at http://www.aiaa.org.
  16. P. Goatin and P. Le Floch, The Riemann problem for a class of resonant hyperbolic systems of balance laws. Ann. Inst. Henri Poincaré, Anal. non linéaire 21 (2004) 881–902.
  17. E. Godlewski, Coupling fluid models. Exploring some features of interfacial coupling, in Proceedings of Finite Volumes for Complex Applications V, Aussois, France, June 8–13 (2008).
  18. E. Godlewski and P.A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: 1. The scalar case. Numer. Math. 97 (2004) 81–130. [CrossRef] [MathSciNet]
  19. E. Godlewski, K.C. Le Thanh and P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems. ESAIM: M2AN 39 (2005) 649–692. [CrossRef] [EDP Sciences] [MathSciNet]
  20. S.K. Godunov, Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47 (1959) 271–300. [MathSciNet]
  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] [MathSciNet]
  22. V. Guillemaud, Modélisation et simulation numérique des écoulements diphasiques par une approche bifluide à deux pressions. Ph.D. Thesis, Université Aix Marseille I, Marseille, France (2007).
  23. P. Helluy, J.-M. Hérard and H. Mathis, A well-balanced approximate Riemann solver for variable cross-section compressible flows. AIAA paper 2009-3888 (2009) available at http://www.aiaa.org.
  24. J.M. Hérard, A rough scheme to couple free and porous media. Int. J. Finite Volumes 3 (2006) available at http://www.latp.univ-mrs.fr/IJFV/.
  25. J.-M. Hérard, A three-phase flow model. Math. Comp. Model. 45 (2007) 432–455.
  26. J.-M. Hérard, Un modèle hyperbolique diphasique bi-fluide en milieu poreux. C. r., Méc. 336 (2008) 650–655.
  27. A.K. Kapila, S.F. Son, J.B. Bdzil, R. Menikoff and D.S. Stewart, Two-phase modeling of a DDT: structure of the velocity relaxation zone. Phys. Fluids 9 (1997) 3885–3897. [CrossRef]
  28. D. Kröner and M.D. Thanh, Numerical solution to compressible flows in a nozzle with variable cross-section. SIAM J. Numer. Anal. 43 (2006) 796–824.
  29. D. Kröner, P. Le Floch and M.D. Thanh, The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. ESAIM: M2AN 42 (2008) 425–442. [CrossRef] [EDP Sciences]
  30. C.A. Lowe, Two-phase shock-tube problems and numerical methods of solution. J. Comput. Phys. 204 (2005) 598–632. [CrossRef] [MathSciNet]
  31. D.W. Schwendeman, C.W. Wahle and A.K. Kapila, The Riemann problem and a high resolution Godunov method for a model of compressible two-phase flow. J. Comput. Phys. 212 (2006) 490–526. [CrossRef] [MathSciNet]

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