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riemann solvers.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Relaxation and numerical approximation of a two-fluid two-pressure diphasic model
Annalisa Ambroso, Christophe Chalons, Frédéric Coquel, Thomas Galié
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 43 / Issue 6 / November 2009

Published online by Cambridge University Press:

09 October 2009, pp. 1063-1097

Print publication:

November 2009
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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.