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

Published online by Cambridge University Press:  09 October 2009

Annalisa Ambroso ,
Christophe Chalons ,
Frédéric Coquel  and
Thomas Galié
Annalisa Ambroso
Affiliation:
DEN/DANS/DM2S/SFME/LETR CEA-Saclay, 91191 Gif-sur-Yvette, France. [email protected]
Christophe Chalons
Affiliation:
DEN/DANS/DM2S/SFME/LETR CEA-Saclay, 91191 Gif-sur-Yvette, France. [email protected] Université Paris 7-Denis Diderot and UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. [email protected]
Frédéric Coquel
Affiliation:
Université Pierre et Marie Curie-Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. [email protected] CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France.
Thomas Galié
Affiliation:
DEN/DANS/DM2S/SFME/LETR CEA-Saclay, 91191 Gif-sur-Yvette, France. [email protected]
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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 termsthat 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, preservesthe natural phase space, and exactly captures the coupling waves between the two phases.Numerical evidences are given to corroborate the validity of our approach.

Keywords

Two-phase flowstwo-fluid two-pressure modelhyperbolic systemsfinite volume methodsrelaxation schemesRiemann solvers.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 6 , November 2009 , pp. 1063 - 1097
Copyright
© EDP Sciences, SMAI, 2009

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