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All issues Volume 42 / No 6 (November-December 2008) ESAIM: M2AN, 42 6 (2008) 991-1019 References
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Issue
ESAIM: M2AN
Volume 42, Number 6, November-December 2008
Page(s) 991 - 1019
DOI https://doi.org/10.1051/m2an:2008036
Published online 25 September 2008
  1. R. Abgrall, Generalization of the Roe scheme for the computation of mixture of perfect gases. Rech. Aérosp. 6 (1988) 31–43. [Google Scholar]
  2. R. Abgrall, How to prevent pressure oscillations in multicomponent flows: A quasi conservative approach. J. Comp. Phys. 125 (1996) 150–160. [Google Scholar]
  3. R. Abgrall and S. Karni, Ghost-fluids for the poor: a single fluid algorithm for multifluids, in Hyperbolic problems: theory, numerics, applications, Vols. I, II (Magdeburg, 2000), Birkhäuser, Basel, Internat. Ser. Numer. Math. 140 (2001) 1–10. [Google Scholar]
  4. R. Abgrall and S. Karni, Computations of compressible multifluids. J. Comp. Phys. 169 (2001) 594–623. [Google Scholar]
  5. R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase flow mixtures. J. Comp. Phys. 186 (2003) 361–396. [Google Scholar]
  6. R. Abgrall, B. N'Konga and R. Saurel, Efficient numerical approximation of compressible multi-material flow for unstructured meshes. Comput. Fluids 4 (2003) 571–605. [CrossRef] [Google Scholar]
  7. I.-L. Chern, J. Glimm, O. McBryan, B. Plohr and S. Yaniv, Front tracking for gas dynamics. J. Comp. Phys. 62 (1986) 83–110. [CrossRef] [Google Scholar]
  8. A. Chertock and A. Kurganov, Conservative locally moving mesh method for multifluid flows. Proceedings of the Fourth International Symposium on Finite Volumes for Complex Applications, Marrakech (2005) 273–284. [Google Scholar]
  9. F. Coquel, K. El Amine, E. Godlewski, B. Perthame and P. Rascle, A numerical method using upwind schemes for the resolution of two-phase flows. J. Comp. Phys. 136 (1997) 272–288. [Google Scholar]
  10. S.F. Davis, An interface tracking method for hyperbolic systems of conservation laws. Appl. Numer. Math. 10 (1992) 447–472. [CrossRef] [MathSciNet] [Google Scholar]
  11. R.P. Fedkiw, T. Aslam, B. Merriman and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comp. Phys. 152 (1999) 457–492. [Google Scholar]
  12. J. Glimm, J.W. Grove, X.L. Li, K.-M. Shyue, Y. Zeng and Q. Zhang, Three-dimensional front tracking. SIAM J. Sci. Comput. 19 (1998) 703–727. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Glimm, X.L. Li, Y. Liu and N. Zhao, Conservative front tracking and level set algorithms. Proc. Natl. Acad. Sci. USA 98 (2001) 14198–14201. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Glimm, Y. Liu, Z. Xu and N. Zhao, Conservative front tracking with improved accuracy. SIAM J. Numer. Anal. 41 (2003) 1926–1947. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Springer-Verlag, New York (1996). [Google Scholar]
  16. E. Godlewski and P.-A. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I. The scalar case. Numer. Math. 97 (2004) 81–130. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Godlewski, K.-C. Le Thanh, 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]
  18. S. Gottlieb, C.-W. Shu and E. Tadmor, High order time discretization methods with the strong stability property. SIAM Rev. 43 (2001) 89–112. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  19. J.-F. Haas and B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181 (1987) 313–336. [Google Scholar]
  20. A. Harten and J.M. Hyman, Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comp. Phys. 50 (1983) 235–269. [Google Scholar]
  21. A. Harten and S. Osher, Uniformly high-order accurate nonoscillatory schemes, I. SIAM J. Numer. Anal. 24 (1987) 279–309. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Harten, S. Osher, B. Engquist and S.R. Chakravarthy, Some results on uniformly high order accurate essentially non-oscillatory schemes. Appl. Numer. Math. 2 (1986) 347–377. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Jenny, B. Mueller and H. Thomann, Correction of conservative Euler solvers for gas mixtures. J. Comp. Phys. 132 (1997) 91–107. [CrossRef] [Google Scholar]
  24. S. Karni, Multicomponent flow calculations by a consistent primitive algorithm. J. Comp. Phys. 112 (1994) 31–43. [Google Scholar]
  25. S. Karni, Compressible bubbles with surface tension, in Sixteenth International Conference on Numerical Methods in Fluid Dynamics (Arcachon, 1998), Springer, Berlin, Lecture Notes in Physics 515 (1998) 506–511. [Google Scholar]
  26. 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]
  27. D. Kröner, Numerical Schemes for Conservation Laws. Wiley, Chichester (1997). [Google Scholar]
  28. A. Kurganov and C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes. Commun. Comput. Phys. 2 (2007) 141–163. [MathSciNet] [Google Scholar]
  29. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comp. Phys. 160 (2000) 241–282. [Google Scholar]
  30. A. Kurganov, S. Noelle and G. Petrova, Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21 (2001) 707–740. [Google Scholar]
  31. B. Larrouturou, How to preserve the mass fractions positivity when computing compressible multi-component flows. J. Comp. Phys. 95 (1991) 59–84. [Google Scholar]
  32. R. LeVeque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics. Cambridge University Press (2002). [Google Scholar]
  33. K.-A. Lie and S. Noelle, On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comput. 24 (2003) 1157–1174. [CrossRef] [MathSciNet] [Google Scholar]
  34. W. Mulder, S. Osher and J.A. Sethian, Computing interface motion in compressible gas dynamics. J. Comp. Phys. 100 (1992) 209–228. [Google Scholar]
  35. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comp. Phys. 87 (1990) 408–463. [Google Scholar]
  36. J.J. Quirk and S. Karni, On the dynamics of a shock-bubble interaction. J. Fluid Mech. 318 (1996) 129–163. [CrossRef] [Google Scholar]
  37. P.L. Roe, Fluctuations and signals – a framework for numerical evolution problems, in Numerical Methods for Fluid Dynamics, Academic Press, New York (1982) 219–257. [Google Scholar]
  38. R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comp. Phys. 150 (1999) 425–467. [Google Scholar]
  39. K.-M. Shyue, An efficient shock-capturing algorithm for compressible multicomponent problems. J. Comp. Phys. 142 (1998) 208–242. [Google Scholar]
  40. K.-M. Shyue, A fluid-mixture type algorithm for compressible multicomponent flow with van der Waals equation of state. J. Comp. Phys. 156 (1999) 43–88. [Google Scholar]
  41. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 (1984) 995–1011. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  42. V. Ton, Improved shock-capturing methods for multicomponent and reacting flows. J. Comp. Phys. 128 (1996) 237–253. [CrossRef] [Google Scholar]
  43. E.F. Toro, Riemann solvers and numerical methods for fluid dynamics. A practical introduction. Second edition, Springer-Verlag, Berlin (1999). [Google Scholar]
  44. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas and Y.-J. Jan, A front-tracking method for the computations of multiphase flow. J. Comp. Phys. 169 (2001) 708–759. [Google Scholar]
  45. B. van Leer, Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov's method. J. Comp. Phys. 32 (1979) 101–136. [NASA ADS] [CrossRef] [Google Scholar]
  46. J. Wackers and B. Koren, Five-equation model for compressible two-fluid flow. Report MAS-E0414, CWI, Amsterdam (2004). Available at http://ftp.cwi.nl/CWIreports/MAS/MAS-E0414.pdf [Google Scholar]
  47. S.-P. Wang, M.H. Anderson, J.G. Oakley, M.L. Corradini and R. Bonazza, A thermodynamically consistent and fully conservative treatment of contact discontinuities for compressible multicomponent flows. J. Comp. Phys. 195 (2004) 528–559. [CrossRef] [Google Scholar]
  48. A. Wardlaw, Underwater explosion test cases. IHTR 2069 (1998). [Google Scholar]

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