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Journal of Nonlinear Science

, Volume 10, Issue 6, pp 639–660 | Cite as

A Hierarchy of Models for Two-Phase Flows

  • F. Bouchut
  • Y. Brenier
  • J. Cortes
  • J.-F.   Ripoll
Article

Summary.

We derive a hierarchy of models for gas-liquid two-phase flows in the limit of infinite density ratio, when the liquid is assumed to be incompressible. The starting model is a system of nonconservative conservation laws with relaxation. At first order in the density ratio, we get a simplified system with viscosity, while at the limit we obtain a system of two conservation laws, the system of pressureless gases with constraint and undetermined pressure. Formal properties of this constraint model are provided, and sticky blocks solutions are introduced. We propose numerical methods for this last model, and the results are compared with the two previous models.

Key words. two-phase flow, conservation laws with relaxation, conservation laws with constraint, pressureless gas, sticky particles and blocks 

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • F. Bouchut
    • 1
  • Y. Brenier
    • 2
  • J. Cortes
    • 3
  • J.-F.   Ripoll
    • 4
  1. 1.Département de Mathématiques et Applications, Ecole Normale Supérieure et CNRS, UMR 8553, 45, rue d'Ulm, 75230 Paris cedex 05, France e-mail: Francois.Bouchut@ens.frFR
  2. 2.Laboratoire d'Analyse Numérique, UMR 7598, Université P. et M. Curie, B.C. 187, Tour 55-65, 5ème étage, 4, place Jussieu, 75252 Paris, France e-mail: brenier@ann.jussieu.frFR
  3. 3.CMLA UMR-8536, Ecole Normale Supérieure de Cachan, Département de Mathématiques, 61, avenue du président Wilson, 94235 Cachan cedex, France e-mail: cortes@cmla.ens-cachan.frFR
  4. 4.Mathématiques Appliquées de Bordeaux UMR 5466, Université de Bordeaux 1 et CNRS, 351, cours de la libération, 33405 Talence cedex, France e-mail: ripoll@math.u-bordeaux.frFR

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