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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
a
Institut Universitaire de France and Universitee de Bordeaux I, Deepartement de Matheematiques Appliqueees,
351 cours de la Libeeration, 33405 Talence, France
b
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
Abstract
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