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

Authors:
Michaël Baudin;Christophe Berthon;Frédéric Coquel;Roland Masson;Quang Huy Tran
Affiliations:
IFP, 1 et 4 avenue de Bois-Préau, 92852, Rueil-Malmaison Cedex, France;Université de Bordeaux I, MAB, 351 cours de la Libération, 33405, Talence Cedex, France;Lab. J.-L. Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252, Paris Cedex 5, France;IFP, 1 et 4 avenue de Bois-Préau, 92852, Rueil-Malmaison Cedex, France;IFP, 1 et 4 avenue de Bois-Préau, 92852, Rueil-Malmaison Cedex, France
Venue:
Numerische Mathematik
Year:
2005

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Abstract

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.