Issue ESAIM: M2AN Volume 43, Number 6, November-December 2009 Page(s) 1063 - 1097 DOI 10.1051/m2an/2009038 Published online 09 October 2009

ESAIM: M2AN 43 (2009) 1063-1097
DOI: 10.1051/m2an/2009038

Relaxation and numerical approximation of a two-fluid two-pressure diphasic model

Annalisa Ambroso¹, Christophe Chalons^{1, 2}, Frédéric Coquel^{3, 4} and Thomas Galié<sup>1

1</sup>  DEN/DANS/DM2S/SFME/LETR CEA-Saclay, 91191 Gif-sur-Yvette, France. annalisa.ambroso@cea.fr
²  Université Paris 7-Denis Diderot and UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. chalons@math.jussieu.fr
³  Université Pierre et Marie Curie-Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. coquel@ann.jussieu.fr
⁴  CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France.

Received May 6, 2008. Revised November 3rd, 2008. Published online October 9, 2009.

Abstract
This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach.

Mathematics Subject Classification. 76T10, 35L60, 76M12.

Key words: Two-phase flows, two-fluid two-pressure model, hyperbolic systems, finite volume methods, relaxation schemes, Riemann solvers.


© EDP Sciences, SMAI 2009

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