@Article{CiCP-15-1237,
author = {Remi Abgrall and Harish Kumar},
title = {Numerical Approximation of a Compressible Multiphase System},
journal = {Communications in Computational Physics},
year = {2014},
volume = {15},
number = {5},
pages = {1237--1265},
abstract = {<p style="text-align: justify;">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 &quot;dual&quot; 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.110313.230913a},
url = {http://global-sci.org/intro/article_detail/cicp/7136.html}
}