Numerical approximation of a compressible multiphase system

Abgrall, Rémi; Kumar, Harish Prasanna Mohan (2014). Numerical approximation of a compressible multiphase system. Communications in Computational Physics, 15(5):1237-1265.

Abstract

The numerical simulation of non conservative systemis a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly fromconservation principles, so that in general, if themodel 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.

Abstract

The numerical simulation of non conservative systemis a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly fromconservation principles, so that in general, if themodel 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.

Statistics

Citations

Dimensions.ai Metrics
6 citations in Web of Science®
5 citations in Scopus®