Relaxation and numerical approximation of a two-fluid two-pressure diphasic model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 6, p. 1063-1097

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.

DOI : https://doi.org/10.1051/m2an/2009038
Classification:  76T10,  35L60,  76M12
Keywords: two-phase flows, two-fluid two-pressure model, hyperbolic systems, finite volume methods, relaxation schemes, Riemann solvers
@article{M2AN_2009__43_6_1063_0,
author = {Ambroso, Annalisa and Chalons, Christophe and Coquel, Fr\'ed\'eric and Gali\'e, Thomas},
title = {Relaxation and numerical approximation of a two-fluid two-pressure diphasic model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {43},
number = {6},
year = {2009},
pages = {1063-1097},
doi = {10.1051/m2an/2009038},
zbl = {pre05636847},
mrnumber = {2588433},
language = {en},
url = {http://www.numdam.org/item/M2AN_2009__43_6_1063_0}
}

Ambroso, Annalisa; Chalons, Christophe; Coquel, Frédéric; Galié, Thomas. Relaxation and numerical approximation of a two-fluid two-pressure diphasic model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 6, pp. 1063-1097. doi : 10.1051/m2an/2009038. http://www.numdam.org/item/M2AN_2009__43_6_1063_0/

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