Free Access
Issue
ESAIM: M2AN
Volume 40, Number 2, March-April 2006
Page(s) 331 - 352
DOI https://doi.org/10.1051/m2an:2006015
Published online 21 June 2006
  1. G. Allaire, S. Clerc and S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids. J. Comput. Phys. 181 (2002) 577–616. [CrossRef] [MathSciNet] [Google Scholar]
  2. T. Barberon and P. Helluy, Finite volume simulations of cavitating flows. In Finite volumes for complex applications, III (Porquerolles, 2002), Lab. Anal. Topol. Probab. CNRS, Marseille (2002) 441–448 (electronic). [Google Scholar]
  3. T. Barberon and P. Helluy, Finite volume simulation of cavitating flows. Comput. Fluids 34 (2005) 832–858. [CrossRef] [Google Scholar]
  4. T. Barberon, P. Helluy and S. Rouy, Practical computation of axisymmetrical multifluid flows. Int. J. on Finite Volumes 1 (2003) 1–34. http://averoes.math.univ-paris13.fr/IJFV [Google Scholar]
  5. F. Bouchut, A reduced stability condition for nonlinear relaxation to conservation laws. J. Hyper. Diff. Eqns 1 (2004) 149–170. [CrossRef] [MathSciNet] [Google Scholar]
  6. Y. Brenier, Averaged multivalued solutions for scalar conservation laws. SIAM J. Numer. Anal. 21 (1984) 1013–1037. [CrossRef] [MathSciNet] [Google Scholar]
  7. Y. Brenier, Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes. C.R. Acad. Sci. Paris Sér. I Math. 308 (1989) 587–589. [Google Scholar]
  8. H.B. Callen, Thermodynamics and an introduction to thermostatistics, second edition. Wiley and Sons (1985). [Google Scholar]
  9. F. Caro, Modélisation et simulation numérique des transitions de phase liquide-vapeur. Ph.D. thesis, École Polytechnique, Paris, France (November 2004). [Google Scholar]
  10. G. Chanteperdrix, P. Villedieu, J.-P. Vila, A compressible model for separated two-phase flows computations. In ASME Fluids Engineering Division Summer Meeting. ASME, Montreal, Canada (July 2002). [Google Scholar]
  11. G.Q. Chen, C. David Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 47 (1994) 787–830. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.-P. Croisille, Contribution à l'étude théorique et à l'approximation par éléments finis du système hyperbolique de la dynamique des gaz multidimensionnelle et multiespèces. Ph.D. thesis, Université Paris VI, France (1991). [Google Scholar]
  13. S. Dellacherie, Relaxation schemes for the multicomponent Euler system. ESAIM: M2AN 37 (2003) 909–936. [CrossRef] [EDP Sciences] [Google Scholar]
  14. L.C. Evans, Entropy and partial differential equations (2004). http://math.berkeley.edu/~evans/entropy.and.PDE.pdf [Google Scholar]
  15. 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] [Google Scholar]
  16. B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations: strictly hyperbolic systems. SIAM J. Math. Anal. 31 (2000) 941–991 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  17. J.-B. Hiriart-Urruty, Optimisation et analyse convexe. Mathématiques, Presses Universitaires de France, Paris (1998). [Google Scholar]
  18. J.-B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of convex analysis. Grundlehren Text Editions, Springer-Verlag, Berlin (2001). [Google Scholar]
  19. S. Jaouen, Étude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase. Ph.D. thesis, Université Paris VI (November 2001). [Google Scholar]
  20. L. Landau and E. Lifchitz, Physique statistique. Physique théorique, Ellipses, Paris (1994). [Google Scholar]
  21. P.D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, in CBMS Regional Conf. Ser. In Appl. Math. 11, Philadelphia, SIAM (1972). [Google Scholar]
  22. P.G. LeFloch and C. Rohde, High-order schemes, entropy inequalities, and nonclassical shocks. SIAM J. Numer. Anal. 37 (2000) 2023–2060. [CrossRef] [MathSciNet] [Google Scholar]
  23. R.J. LeVeque and M. Pelanti, A class of approximate Riemann solvers and their relation to relaxation schemes. J. Comput. Phys. 172 (2001) 572–591. [CrossRef] [MathSciNet] [Google Scholar]
  24. T.P. Liu, The Riemann problem for general systems of conservation laws. J. Differ. Equations 56 (1975) 218–234. [Google Scholar]
  25. Y. Lucet, A fast computational algorithm for the Legendre-Fenchel transform. Comput. Optim. Appl. 6 (1996) 27–57. [MathSciNet] [Google Scholar]
  26. Y. Lucet, Faster than the fast Legendre transform, the linear-time Legendre transform. Numer. Algorithms 16 (1998) 171–185. [CrossRef] [Google Scholar]
  27. P.-A. Mazet and F. Bourdel, Multidimensional case of an entropic variational formulation of conservative hyperbolic systems. Rech. Aérospatiale 5 (1984) 369–378. [Google Scholar]
  28. R. Menikoff and B.J. Plohr, The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61 (1989) 75–130. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  29. B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property. SIAM J. Numer. Anal. 27 (1990) 1405–1421. [CrossRef] [MathSciNet] [Google Scholar]
  30. R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425–467. [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