The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems
Laboratoire Jacques-Louis Lions, Université Pierre et
Marie Curie, 75252 Paris Cedex 05, France. email@example.com
2 CEA, BP 12, 91680 Bruyères le Chatel, France. firstname.lastname@example.org
Revised: 16 November 2004
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.
Mathematics Subject Classification: 35L50 / 35L65 / 65M12 / 65M30 / 65-04 / 76M12
Key words: Conservation laws / Riemann problem / boundary value problems / interface coupling / finite volume schemes.
© EDP Sciences, SMAI, 2005