Free Access
Issue
ESAIM: M2AN
Volume 40, Number 4, July-August 2006
Page(s) 735 - 764
DOI https://doi.org/10.1051/m2an:2006032
Published online 15 November 2006
  1. R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186 (2003) 361–396. [CrossRef] [MathSciNet]
  2. M. Baudin, C. Berthon, F. Coquel, R. Masson and Q.H. Tran, A relaxation method for two-phase flow models with hydrodynamic closure law. Numer. Math. 99 (2005) 411–440. [CrossRef] [MathSciNet]
  3. M. Baudin, F. Coquel and Q.H. Tran, A semi-implicit relaxation scheme for modeling two-phase flow in a pipeline. SIAM J. Sci. Comput. 27 (2005) 914–936. [CrossRef] [MathSciNet]
  4. K.H. Bendiksen, An experimental investigation of the motion of long bubbles in inclined tubes. Int. J. Multiphas. Flow 10 (1984) 467–483. [CrossRef]
  5. S. Benzoni-Gavage, Analyse numérique des modèles hydrodynamiques d'écoulements diphasiques instationnaires dans les réseaux de production pétrolière. Thèse ENS Lyon, France (1991).
  6. J. Cortes, A. Debussche and I. Toumi, A density perturbation method to study the eigenstructure of two-phase flow equation systems, J. Comput. Phys. 147 (1998) 463–484.
  7. S. Evje and K.K. Fjelde, Hybrid flux-splitting schemes for a two-phase flow model. J. Comput. Phys. 175 (2002) 674–201. [CrossRef]
  8. S. Evje and K.K. Fjelde, On a rough AUSM scheme for a one-dimensional two-phase model. Comput. Fluids 32 (2003) 1497–1530. [CrossRef] [MathSciNet]
  9. S. Evje and T. Flåtten, Hybrid flux-splitting schemes for a common two-fluid model. J. Comput. Phys. 192 (2003) 175–210. [CrossRef]
  10. I. Faille and E. Heintzé, A rough finite volume scheme for modeling two-phase flow in a pipeline. Comput. Fluids 28 (1999) 213–241. [CrossRef] [MathSciNet]
  11. K.K. Fjelde and K.H. Karlsen, High-resolution hybrid primitive-conservative upwind schemes for the drift-flux model. Comput. Fluids 31 (2002) 335–367. [CrossRef]
  12. F. França and R.T. Lahey, Jr., The use of drift-flux techniques for the analysis of horizontal two-phase flows. Int. J. Multiphas. Flow 18 (1992) 787–801. [CrossRef]
  13. A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357–393. [NASA ADS] [CrossRef] [MathSciNet]
  14. S. Jin and Z.P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Commun. Pur. Appl. Math. 48 (1995) 235–276. [CrossRef] [MathSciNet]
  15. 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]
  16. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge, UK (2002).
  17. J.M. Masella, Q.H. Tran, D. Ferre and C. Pauchon, Transient simulation of two-phase flows in pipes. Int. J. Multiphas. Flow 24 (1998) 739–755. [CrossRef]
  18. S.T. Munkejord, S. Evje and T. Flåtten, The multi-stage centred-scheme approach applied to a drift-flux two-phase flow model. Int. J. Numer. Meth. Fl. 52 (2006) 679–705. [CrossRef]
  19. A. Murrone and H. Guillard, A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202 (2005) 664–698. [CrossRef] [MathSciNet]
  20. S. Osher, Riemann solvers, the entropy condition, and difference approximations. SIAM J. Numer. Anal. 21 (1984) 217–235. [CrossRef] [MathSciNet]
  21. V.H. Ransom and D.L. Hicks, Hyperbolic two-pressure models for two-phase flow. J. Comput. Phys. 53 (1984) 124–151. [CrossRef] [MathSciNet]
  22. P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357–372. [NASA ADS] [CrossRef] [MathSciNet]
  23. J.E. Romate, An approximate Riemann solver for a two-phase flow model with numerically given slip relation. Comput. Fluids 27 (1998) 455–477. [CrossRef] [MathSciNet]
  24. L. Sainsaulieu, Finite volume approximation of two-phase fluid flow based on an approximate Roe-type Riemann solver. J. Comput. Phys. 121 (1995) 1–28. [CrossRef] [MathSciNet]
  25. R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425–467. [CrossRef] [MathSciNet]
  26. H.B. Stewart and B. Wendroff, Review article; Two-phase flow: models and methods. J. Comput. Phys. 56 (1984) 363–409.
  27. V.A. Titarev and E.F. Toro, MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements. Int. J. Numer. Meth. Fl. 49 (2005) 117–147. [CrossRef]
  28. E.F. Toro, Riemann solvers and numerical methods for fluid dynamics, 2nd edn. Springer-Verlag, Berlin (1999).
  29. I. Toumi, An upwind numerical method for two-fluid two-phase flow models. Nucl. Sci. Eng. 123 (1996) 147–168.
  30. I. Toumi and D. Caruge, An implicit second-order numerical method for three-dimensional two-phase flow calculations. Nucl. Sci. Eng. 130 (1998) 213–225.
  31. I. Toumi and A. Kumbaro, An approximate linearized Riemann solver for a two-fluid model. J. Comput. Phys. 124 (1996) 286–300. [CrossRef] [MathSciNet]
  32. B. van Leer, Towards the ultimate conservative difference scheme IV. New approach to numerical convection. J. Comput. Phys. 23 (1977) 276–299. [NASA ADS] [CrossRef]
  33. N. Zuber and J.A. Findlay, Average volumetric concentration in two-phase flow systems. J. Heat Transfer 87 (1965) 453–468.

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