We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem. We discuss both approaches in the case of the coupling of two fluid models at a material contact discontinuity, the models being the usual gas dynamics equations with different equations of state. We also study the coupling of two-temperature plasma fluid models and illustrate the approach by numerical simulations.
Mots-clés : conservation laws, Riemann problem, boundary value problems, interface coupling, finite volume schemes
@article{M2AN_2005__39_4_649_0,
author = {Godlewski, Edwige and Thanh, Kim-Claire Le and Raviart, Pierre-Arnaud},
title = {The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : {II.} {The} case of systems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {649--692},
publisher = {EDP-Sciences},
volume = {39},
number = {4},
year = {2005},
doi = {10.1051/m2an:2005029},
mrnumber = {2165674},
zbl = {1095.65084},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005029/}
}
TY - JOUR AU - Godlewski, Edwige AU - Thanh, Kim-Claire Le AU - Raviart, Pierre-Arnaud TI - The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 649 EP - 692 VL - 39 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005029/ DO - 10.1051/m2an:2005029 LA - en ID - M2AN_2005__39_4_649_0 ER -
%0 Journal Article %A Godlewski, Edwige %A Thanh, Kim-Claire Le %A Raviart, Pierre-Arnaud %T The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 649-692 %V 39 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005029/ %R 10.1051/m2an:2005029 %G en %F M2AN_2005__39_4_649_0
Godlewski, Edwige; Thanh, Kim-Claire Le; Raviart, Pierre-Arnaud. The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 649-692. doi : 10.1051/m2an:2005029. http://www.numdam.org/articles/10.1051/m2an:2005029/
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