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A relaxation method for two-phase flow models with hydrodynamic closure law

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Summary.

This paper is devoted to the numerical approximation of the solutions of a system of conservation laws arising in the modeling of two-phase flows in pipelines. The PDEs are closed by two highly nonlinear algebraic relations, namely, a pressure law and a hydrodynamic one. The severe nonlinearities encoded in these laws make the classical approximate Riemann solvers virtually intractable at a reasonable cost of evaluation. We propose a strategy for relaxing solely these two nonlinearities. The relaxation system we introduce is of course hyperbolic but all associated eigenfields are linearly degenerate. Such a property not only makes it trivial to solve the Riemann problem but also enables us to enforce some further stability requirements, in addition to those coming from a Chapman-Enskog analysis. The new method turns out to be fairly simple and robust while achieving desirable positivity properties on the density and the mass fractions. Extensive numerical evidences are provided.

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Authors and Affiliations

  1. IFP, 1 et 4 avenue de Bois-Préau, 92852, Rueil-Malmaison Cedex, France

    Michaël Baudin,  Roland Masson & Quang Huy Tran

  2. MAB, Université de Bordeaux I, 351 cours de la Libération, 33405, Talence Cedex, France

    Christophe Berthon

  3. Lab. J.-L. Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252, Paris Cedex 5

    Frédéric Coquel

Authors
  1. Michaël Baudin
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  2. Christophe Berthon
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  3. Frédéric Coquel
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  4. Roland Masson
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  5. Quang Huy Tran
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Mathematics Subject Classification (1991): 76T10, 76N15, 35L65, 65M06

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Baudin, M., Berthon, C., Coquel, F. et al. A relaxation method for two-phase flow models with hydrodynamic closure law. Numer. Math. 99, 411–440 (2005). https://doi.org/10.1007/s00211-004-0558-1

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  • DOI: https://doi.org/10.1007/s00211-004-0558-1

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