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Discrete equations for physical and numerical compressible multiphase mixtures

Summary: Discrete equations for physical and numerical compressible
multiphase mixtures
Reemi Abgrall a,*,1
, Richard Saurel b,2
Institut Universitaire de France and Universitee de Bordeaux I, Deepartement de Matheematiques Appliqueees,
351 cours de la Libeeration, 33405 Talence, France
Institut Universitaire de France and PolytechÕMarseille, IUSTI, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
Received 4 July 2002; received in revised form 21 November 2002; accepted 24 December 2002
We have recently proposed, in [21], a compressible two-phase unconditionally hyperbolic model able to deal with a
wide range of applications: interfaces between compressible materials, shock waves in condensed multiphase mixtures,
homogeneous two-phase flows (bubbly and droplet flows) and cavitation in liquids. One of the difficulties of the model,
as always in this type of physical problems, was the occurrence of non-conservative products. In [21], we have proposed
a discretisation technique that was without any ambiguity only in the case of material interfaces, not in the case of
shock waves. This model was extended to several space dimensions in [24], In this paper, thanks to a deeper analysis of
the model, we propose a class of schemes that are able to converge to the correct solution even when shock waves
interact with volume fraction discontinuities. This analysis provides a more accurate estimate of closure terms, but also
an accurate resolution method for the conservative fluxes as well as non-conservative terms even for situations involving


Source: Abgrall, Rémi - Institut de Mathematiques de Bordeaux, Université Bordeaux


Collections: Mathematics