Extension of interface coupling to general Lagrangian systems

We study the coupling of two gas dynamics systems in Lagrangian coordinates at the interface x = 0. The coupling condition was formalized in [9, 10] by requiring that two boundary value problems should be well-posed, and it yields as far as possible the continuity of the solution at the interface. In this work we prove that we may choose the variables we transmit and extend the theory to Lagrangian systems of different sizes. The coupling condition is expressed in terms of Riemann problems. This is well suited for the numerical methods we are implementing and adapted to Lagrangian systems since the sign of the wave speeds is known, which enables us to solve the coupled Riemann problem.