The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density and additional variables are exhibited. It is shown first that a standard conservative formulation of above mentioned schemes enables to predict “perfectly” unsteady contact discontinuities on coarse meshes, when the equation of state (EOS) belongs to the first class. On the basis of previous work issuing from literature, an almost conservative though modified version of the scheme is proposed to deal with EOS in the second or third class. Numerical evidence shows that the accuracy of approximations of discontinuous solutions of standard Riemann problems is strengthened on coarse meshes, but that convergence towards the right shock solution may be lost in some cases involving complex EOS in the third class. Hence, a blend scheme is eventually proposed to benefit from both properties (“perfect” representation of contact discontinuities on coarse meshes, and correct convergence on finer meshes). Computational results based on an approximate Godunov scheme are provided and discussed.
Mots clés : Godunov scheme, Euler system, contact discontinuities, thermodynamics, conservative schemes
@article{M2AN_2002__36_6_1133_0,
author = {Gallou\"et, Thierry and H\'erard, Jean-Marc and Seguin, Nicolas},
title = {A hybrid scheme to compute contact discontinuities in one-dimensional {Euler} systems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1133--1159},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
doi = {10.1051/m2an:2003009},
mrnumber = {1958662},
zbl = {1137.65419},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003009/}
}
TY - JOUR AU - Gallouët, Thierry AU - Hérard, Jean-Marc AU - Seguin, Nicolas TI - A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 1133 EP - 1159 VL - 36 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003009/ DO - 10.1051/m2an:2003009 LA - en ID - M2AN_2002__36_6_1133_0 ER -
%0 Journal Article %A Gallouët, Thierry %A Hérard, Jean-Marc %A Seguin, Nicolas %T A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 1133-1159 %V 36 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003009/ %R 10.1051/m2an:2003009 %G en %F M2AN_2002__36_6_1133_0
Gallouët, Thierry; Hérard, Jean-Marc; Seguin, Nicolas. A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 6, pp. 1133-1159. doi : 10.1051/m2an:2003009. http://www.numdam.org/articles/10.1051/m2an:2003009/
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