EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 43 / No 6 (November-December 2009) ESAIM: M2AN, 43 6 (2009) 1063-1097 References
Free Access
Issue
ESAIM: M2AN
Volume 43, Number 6, November-December 2009
Page(s) 1063 - 1097
DOI https://doi.org/10.1051/m2an/2009038
Published online 09 October 2009
  1. R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186 (2003) 361–396. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Ambroso, C. Chalons, F. Coquel, T. Galié, E. Godlewski, P.-A Raviart and N. Seguin, The drift-flux asymptotic limit of barotropic two-phase two-pressure models. Comm. Math. Sci. 6 (2008) 521–529. [Google Scholar]
  3. N. Andrianov, Analytical and numerical investigation of two-phase flows. Ph.D. Thesis, Univ. Magdeburg, Germany (2003). [Google Scholar]
  4. 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]
  5. N. Andrianov, R. Saurel and G. Warnecke, A simple method for compressible multiphase mixtures and interfaces. Int. J. Numer. Methods Fluids 41 (2003) 109–131. [CrossRef] [Google Scholar]
  6. M.R. Baer and J.W. Nunziato, A two phase mixture theory for the deflagration to detonation (DDT) transition in reactive granular materials. Int. J. Multiphase Flows 12 (1986) 861–889. [CrossRef] [Google Scholar]
  7. C. Berthon, B. Braconnier, B. Nkonga, Numerical approximation of a degenerate non-conservative multifluid model: relaxation scheme. Int. J. Numer. Methods Fluids 48 (2005) 85–90. [CrossRef] [Google Scholar]
  8. 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]
  9. B. Braconnier, Modélisation numérique d'écoulements multiphasiques pour des fluides compressibles, non miscibles et soumis aux effets capillaires. Ph.D. Thesis, Université Bordeaux I, France (2007). [Google Scholar]
  10. T. Buffard, T. Gallouët and J.M. Hérard, A sequel to a rough Godunov scheme. Application to real gas flows. Comput. Fluids 29 (2000) 813–847. [CrossRef] [MathSciNet] [Google Scholar]
  11. C.E. Castro and E.F. Toro, A Riemann solver and upwind methods for a two-phase flow model in nonconservative form. Int. J. Numer. Methods Fluids 50 (2006) 275–307. [CrossRef] [Google Scholar]
  12. C. Chalons and F. Coquel, Navier-Stokes equations with several independent pressure laws and explicit predictor-corrector schemes. Numer. Math. 101 (2005) 451–478. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. Chalons and J.F. Coulombel, Relaxation approximation of the Euler equations. J. Math. Anal. Appl. 348 (2008) 872–893. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Coquel, K. El Amine, E. Godlewski, B. Perthame and P. Rascle, Numerical methods using upwind schemes for the resolution of two-phase flows. J. Comput. Phys. 136 (1997) 272–288. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Coquel, E. Godlewski, A. In, B. Perthame and P. Rascle, Some new Godunov and relaxation methods for two phase flows, in Proceedings of the International Conference on Godunov methods: theory and applications, Kluwer Academic, Plenum Publisher (2001). [Google Scholar]
  16. F. Coquel, T. Gallouët, J.M. Hérard and N. Seguin, Closure laws for a two-phase two-pressure model. C. R. Math. 334 (2002) 927–932. [Google Scholar]
  17. F. Dubois and P.G. LeFloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws. J. Differ. Equ. 71 (1988) 93–122. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Embid and M. Baer, Mathematical analysis of a two-phase continuum mixture theory. Contin. Mech. Thermodyn. 4 (1992) 279–312. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. Galié, Couplage interfacial de modèles en dynamique des fluides. Application aux écoulements diphasiques. Ph.D. Thesis, Université Pierre et Marie Curie, France (2008). [Google Scholar]
  20. T. Gallouët, J.M. Hérard and N. Seguin, Numerical modeling of two-phase flows using the two-fluid two-pressure approach. Math. Mod. Meth. Appl. Sci. 14 (2004) 663–700. [Google Scholar]
  21. S. Gavrilyuk and R. Saurel, Mathematical and numerical modeling of two-phase compressible flows with micro-inertia. J. Comput. Phys. 175 (2002) 326–360. [Google Scholar]
  22. J. Glimm, D. Saltz and D.H. Sharp, Two phase flow modelling of a fluid mixing layer. J. Fluid Mech. 378 (1999) 119–143. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Goatin and P.G. LeFloch, The Riemann problem for a class of resonant nonlinear systems of balance laws. Ann. Inst. H. Poincaré, Anal. Non linéaire 21 (2004) 881–902. [Google Scholar]
  24. E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Springer-Verlag (1996). [Google Scholar]
  25. V. Guillemaud, Modélisation et simulation numérique des écoulements diphasiques par une approche bifluide à deux pressions. Ph.D. Thesis, Université de Provence, Aix-Marseille 1, France (2007). [Google Scholar]
  26. S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48 (1995) 235–276. [Google Scholar]
  27. A.K. Kapila, S.F. Son, J.B. Bdzil, R. Menikoff and D.S. Stewart, Two phase modeling of DDT: structure of the velocity-relaxation zone. Phys. Fluids 9 (1997) 3885–3897. [Google Scholar]
  28. S. Karni, E. Kirr, A. Kurganov and G. Petrova, Compressible two-phase flows by central and upwind schemes. ESAIM: M2AN 38 (2004) 477–493. [CrossRef] [EDP Sciences] [Google Scholar]
  29. P.G. LeFloch, Entropy weak solutions to nonlinear hyperbolic systems in nonconservative form. Commun. Partial Differ. Equ. 13 (1988) 669–727. [Google Scholar]
  30. P.G. LeFloch, Shock waves for nonlinear hyperbolic systems in nonconservative form. Preprint # 593, Institute for Math. and its Appl., Minneapolis, USA (1989). [Google Scholar]
  31. P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Comm. Math. Sci. 1 (2003) 763–796. [Google Scholar]
  32. S.T. Munkejord, Comparison of Roe-type methods for solving the two-fluid model with and without pressure relaxation. Comput. Fluids 36 (2007) 1061–1080. [CrossRef] [Google Scholar]
  33. V.H. Ransom, Numerical benchmark tests, in Multiphase science and technology, Vol. 3, G.F. Hewitt, J.M. Delhaye and N. Zuber Eds., Washington, USA, Hemisphere/Springer (1987) 465–467. [Google Scholar]
  34. V.V Rusanov, Calculation of interaction of non-steady shock waves with obstacles. J. Comp. Math. Phys. USSR 1 (1961) 267–279. [Google Scholar]
  35. R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425–467. [Google Scholar]
  36. R. Saurel and O. Lemetayer, A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J. Fluid Mech. 431 (2001) 239–271. [Google Scholar]
  37. D.W. Schwendeman, C.W. Wahle and A.K Kapila, The Riemann problem and 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