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The numerical interface coupling of nonlinearhyperbolic systems of conservation laws: II. The case of systems

Published online by Cambridge University Press:  15 August 2005

Edwige Godlewski ,
Kim-Claire Le Thanh  and
Pierre-Arnaud Raviart
Edwige Godlewski
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France. godlewski@ann.jussieu.fr
Kim-Claire Le Thanh
Affiliation:
CEA, BP 12, 91680 Bruyères le Chatel, France. kim-claire.le-thanh@cea.fr
Pierre-Arnaud Raviart
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France. godlewski@ann.jussieu.fr
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Abstract

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.

Keywords

Conservation lawsRiemann problemboundary value problemsinterface couplingfinite volume schemes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 4 , July 2005 , pp. 649 - 692
Copyright
© EDP Sciences, SMAI, 2005

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