Geodesic
The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 4, pp. 649-692

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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 : 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 
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     title = {The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : {II.} {The} case of systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {649--692},
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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 , Tome 39 (2005) no. 4, pp. 649-692. doi: 10.1051/m2an:2005029

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