Volume 15, Issue 5
Numerical Approximation of a Compressible Multiphase System

Remi Abgrall & Harish Kumar

Commun. Comput. Phys., 15 (2014), pp. 1237-1265.

Published online: 2014-05

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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 a hybridation of Glimm scheme and Roe scheme.

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@Article{CiCP-15-1237, author = {}, title = {Numerical Approximation of a Compressible Multiphase System}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1237--1265}, 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 a hybridation of Glimm scheme and Roe scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.110313.230913a}, url = {http://global-sci.org/intro/article_detail/cicp/7136.html} }
TY - JOUR T1 - Numerical Approximation of a Compressible Multiphase System JO - Communications in Computational Physics VL - 5 SP - 1237 EP - 1265 PY - 2014 DA - 2014/05 SN - 15 DO - http://doi.org/10.4208/cicp.110313.230913a UR - https://global-sci.org/intro/article_detail/cicp/7136.html KW - AB -

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 a hybridation of Glimm scheme and Roe scheme.

Remi Abgrall & Harish Kumar. (2020). Numerical Approximation of a Compressible Multiphase System. Communications in Computational Physics. 15 (5). 1237-1265. doi:10.4208/cicp.110313.230913a
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