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, Volume 39 (2005) no. 4, p. 649-692

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.

DOI : https://doi.org/10.1051/m2an:2005029
Classification:  35L50,  35L65,  65M12,  65M30,  65-04,  76M12
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     pages = {649-692},
     doi = {10.1051/m2an:2005029},
     zbl = {1095.65084},
     mrnumber = {2165674},
     language = {en},
     url = {http://www.numdam.org/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, Volume 39 (2005) no. 4, pp. 649-692. doi : 10.1051/m2an:2005029. http://www.numdam.org/item/M2AN_2005__39_4_649_0/

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