Free Access
Issue
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
Page(s) 411 - 442
DOI https://doi.org/10.1051/m2an/2011039
Published online 26 October 2011
  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. 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. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  4. 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] [Google Scholar]
  5. K.H. Bendiksen, D. Malnes, R. Moe and S. Nuland, The dynamic two-fluid model OLGA: theory and application. SPE Prod. Eng. 6 (1991) 171–180. [Google Scholar]
  6. D. Bestion, The physical closure laws in the CATHARE code. Nucl. Eng. Des. 124 (1990) 229–245. [CrossRef] [Google Scholar]
  7. C.-H. Chang and M.-S. Liou, A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme. J. Comput. Phys. 225 (2007) 850–873. [Google Scholar]
  8. G.-Q. Chen, C.D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy. Commun. Pure Appl. Math. 47 (1994) 787–830. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Cinnella, Roe-type schemes for dense gas flow computations. Comput. Fluids 35 (2006) 1264–1281. [CrossRef] [Google Scholar]
  10. 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. Comput. Phys. 136 (1997) 272–288. [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Coquel, Q.L. Nguyen, M. Postel and Q.H. Tran, Entropy-satisfying relaxation method with large time-steps for Euler IBVPs. Math. Comput. 79 (2010) 1493–1533. [CrossRef] [Google Scholar]
  12. S. Evje and K.K. Fjelde, Relaxation schemes for the calculation of two-phase flow in pipes. Math. Comput. Modelling 36 (2002) 535–567. [CrossRef] [MathSciNet] [Google Scholar]
  13. S. Evje and T. Flåtten, Hybrid flux-splitting schemes for a common two-fluid model. J. Comput. Phys. 192 (2003) 175–210. [CrossRef] [Google Scholar]
  14. S. Evje and T. Flåtten, Hybrid central-upwind schemes for numerical resolution of two-phase flows. ESAIM: M2AN 39 (2005) 253–273. [CrossRef] [EDP Sciences] [Google Scholar]
  15. S. Evje and T. Flåtten, On the wave structure of two-phase flow models. SIAM J. Appl. Math. 67 (2007) 487–511. [CrossRef] [Google Scholar]
  16. T. Flåtten and S.T. Munkejord, The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model. ESAIM: M2AN 40 (2006) 735–764. [CrossRef] [EDP Sciences] [Google Scholar]
  17. T. Flåtten, A. Morin and S.T. Munkejord, Wave propagation in multicomponent flow models. SIAM J. Appl. Math. 70 (2010) 2861–2882. [CrossRef] [MathSciNet] [Google Scholar]
  18. T. Flåtten, A. Morin and S.T. Munkejord, On solutions to equilibrium problems for systems of stiffened gases. SIAM J. Appl. Math. 71 (2011) 41–67. [CrossRef] [MathSciNet] [Google Scholar]
  19. H. Guillard and F. Duval, A Darcy law for the drift velocity in a two-phase flow model. J. Comput. Phys. 224 (2007) 288–313. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Commun. Pure Appl. Math. 48 (1995) 235–276. [CrossRef] [MathSciNet] [Google Scholar]
  21. K.H. Karlsen, C. Klingenberg and N.H. Risebro, A relaxation scheme for conservation laws with a discontinuous coefficient. Math. Comput. 73 (2004) 1235–1259. [Google Scholar]
  22. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge, UK (2002). [Google Scholar]
  23. T.-P. Liu, Hyperbolic conservation laws with relaxation. Commun. Math. Phys. 108 (1987) 153–175. [CrossRef] [MathSciNet] [Google Scholar]
  24. P.J. Martínez Ferrer, Numerical and mathematical analysis of a five-equation model for two-phase flow. Master's thesis, SINTEF Energy Research, Trondheim, Norway (2010). Available from http://www.sintef.no/Projectweb/CO2-Dynamics/Publications/. [Google Scholar]
  25. J.M. Masella, Q.H. Tran, D. Ferre and C. Pauchon, Transient simulation of two-phase flows in pipes. Int. J. Multiphase Flow 24 (1998) 739–755. [CrossRef] [Google Scholar]
  26. S.T. Munkejord, Partially-reflecting boundary conditions for transient two-phase flow. Commun. Numer. Meth. Eng. 22 (2007) 781–795. [CrossRef] [Google Scholar]
  27. S.T. Munkejord, S. Evje and T. Flåtten, A MUSTA scheme for a nonconservative two-fluid model. SIAM J. Sci. Comput. 31 (2009) 2587–2622. [CrossRef] [MathSciNet] [Google Scholar]
  28. 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] [Google Scholar]
  29. R. Natalini, Recent results on hyperbolic relaxation problems. Analysis of systems of conservation laws, in Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 99. Chapman & Hall/CRC, Boca Raton, FL (1999) 128–198. [Google Scholar]
  30. H. Paillère, C. Corre and J.R. Carcía Gascales, On the extension of the AUSM+ scheme to compressible two-fluid models. Comput. Fluids 32 (2003) 891–916. [CrossRef] [MathSciNet] [Google Scholar]
  31. L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25 (2005) 129–155. [Google Scholar]
  32. V.H. Ransom, Faucet Flow, in Numerical Benchmark Tests, Multiph. Sci. Technol. 3, edited by G.F. Hewitt, J.M. Delhaye and N. Zuber. Hemisphere-Springer, Washington, USA (1987) 465–467. [Google Scholar]
  33. P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357–372. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  34. 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]
  35. R. Saurel, F. Petitpas and R. Abgrall, Modelling phase transition in metastable liquids: application to cavitating and flashing flows. J. Fluid Mech. 607 (2008) 313–350. [CrossRef] [MathSciNet] [Google Scholar]
  36. H.B. Stewart and B. Wendroff, Two-phase flow: models and methods. J. Comput. Phys. 56 (1984) 363–409. [CrossRef] [MathSciNet] [Google Scholar]
  37. J.H. Stuhmiller, The influence of interfacial pressure forces on the character of two-phase flow model equations. Int. J. Multiphase Flow 3 (1977) 551–560. [CrossRef] [Google Scholar]
  38. I. Tiselj and S. Petelin, Modelling of two-phase flow with second-order accurate scheme. J. Comput. Phys. 136 (1997) 503–521. [CrossRef] [Google Scholar]
  39. I. Toumi, A weak formulation of Roe's approximate Riemann solver. J. Comput. Phys. 102 (1992) 360–373. [CrossRef] [MathSciNet] [Google Scholar]
  40. I. Toumi, An upwind numerical method for two-fluid two-phase flow models. Nucl. Sci. Eng. 123 (1996) 147–168. [Google Scholar]
  41. Q.H. Tran, M. Baudin and F. Coquel, A relaxation method via the Born-Infeld system. Math. Mod. Methods Appl. Sci. 19 (2009) 1203–1240. [CrossRef] [MathSciNet] [Google Scholar]
  42. J.A. Trapp and R.A. Riemke, A nearly-implicit hydrodynamic numerical scheme for two-phase flows. J. Comput. Phys. 66 (1986) 62–82. [CrossRef] [MathSciNet] [Google Scholar]
  43. B. van Leer, Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second-order scheme. J. Comput. Phys. 14 (1974) 361–370. [NASA ADS] [CrossRef] [Google Scholar]
  44. B. van Leer, Towards the ultimate conservative difference scheme IV. A new approach to numerical convection. J. Comput. Phys. 23 (1977) 276–299. [NASA ADS] [CrossRef] [Google Scholar]
  45. WAHA3 Code Manual, JSI Report IJS-DP-8841. Jožef Stefan Institute, Ljubljana, Slovenia (2004). [Google Scholar]
  46. A. Zein, M. Hantke and G. Warnecke, Modeling phase transition for compressible two-phase flows applied to metastable liquids. J. Comput. Phys. 229 (2010) 2964–2998. [CrossRef] [MathSciNet] [Google Scholar]
  47. N. Zuber and J.A. Findlay, Average volumetric concentration in two-phase flow systems. J. Heat Transfer 87 (1965) 453–468. [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