We study the theoretical and numericalcoupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the couplingpreserves in a weak sense the continuity of the solution at the interfacewithout imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling inthe 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 ofstate. We also study the coupling of two-temperature plasma fluid models and illustrate the approach by numericalsimulations.
