Coupled general Riemann problems for the Euler equations

We introduce a novel method for systems of conservation laws coupled at a sharp interface based on generalized Riemann problems. This method yields a piecewise-linear in time approximation of the solution at the interface, thus, descynchronising the solvers for the coupled systems. We apply this framework to a problem of compressible Euler equations coupled via a gas generator and prove its solvability. Finally, we conduct numerical experiments and show that our algorithm performs at correct convergence rates.