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A two-fluid hyperbolic model in a porous medium

Published online by Cambridge University Press:  10 May 2010

Laëtitia Girault  and
Jean-Marc Hérard
Laëtitia Girault
Affiliation:
EDF, R&D, Fluid Dynamics, Power Generation and Environment, 6 quai Watier, 78400 Chatou, France. [email protected] Centre de Mathématiques et Informatique, LATP, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France.
Jean-Marc Hérard
Affiliation:
EDF, R&D, Fluid Dynamics, Power Generation and Environment, 6 quai Watier, 78400 Chatou, France. [email protected]
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Abstract

The paper is devoted to the computation of two-phase flows in a porous mediumwhen applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them correspondingto solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme,are shown to give wrong approximations in some cases involving sharp porous profiles.The third one, which is an extension of a scheme proposed by Kröner and Thanh [SIAM J. Numer. Anal. 43 (2006) 796–824]for the computation of single phase flows in varying cross section ducts,provides fair results in all situations. Properties of schemes and numerical results are presented. Analytic tests enable to compute the L 1 norm of the error.

Keywords

Porous mediumwell-balanced schemeanalytic solutionconvergence ratetwo-phase flow.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 6 , November 2010 , pp. 1319 - 1348
Copyright
© EDP Sciences, SMAI, 2010

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