EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 44 / No 6 (November-December 2010) ESAIM: M2AN, 44 6 (2010) 1319-1348 References
Free Access
Issue
ESAIM: M2AN
Volume 44, Number 6, November-December 2010
Page(s) 1319 - 1348
DOI https://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). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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/. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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. [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. 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). [Google Scholar]
  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. [Google Scholar]
  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/. [Google Scholar]
  25. J.-M. Hérard, A three-phase flow model. Math. Comp. Model. 45 (2007) 432–455. [Google Scholar]
  26. J.-M. Hérard, Un modèle hyperbolique diphasique bi-fluide en milieu poreux. C. r., Méc. 336 (2008) 650–655. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  30. C.A. Lowe, Two-phase shock-tube problems and numerical methods of solution. J. Comput. Phys. 204 (2005) 598–632. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you