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Numerical Approximation of a Compressible Multiphase System

Published online by Cambridge University Press:  03 June 2015

Remi Abgrall  and
Harish Kumar
Remi Abgrall*
Affiliation:
INRIA and Institut de Mathématiques de Bordeaux, Institut Polytechnique de Bordeaux, 200 route de la Vieille Tour, 33 405 Talence, France
Harish Kumar*
Affiliation:
Department of Mathematics, IIT Delhi, New Delhi, India-110016
*
Corresponding author.Email:remi.abgrall@inria.fr
Email:hkumar@maths.iitd.ac.in
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Abstract

The numerical simulation of non conservative system is a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly from conservation principles, so that in general, if the model description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [1]. In this paper we are interested in the “dual” problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme.

Keywords

65M0665M0865M1235L6035L6535L67Non conservative systemsnumerical approximationGlimm’s schemeRoe’s scheme
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 5 , May 2014 , pp. 1237 - 1265
Copyright
Copyright © Global Science Press Limited 2014

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