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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {649-692},
doi = {10.1051/m2an:2005029},
mrnumber = {2165674},
zbl = {1095.65084},
language = {en},
url = {http://dml.mathdoc.fr/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 649-692. doi : 10.1051/m2an:2005029. http://gdmltest.u-ga.fr/item/M2AN_2005__39_4_649_0/
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