A Robust and Entropy-Satisfying Numerical Scheme for Fluid Flows in Discontinuous Nozzles

We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is based on a piecewise constant discretization of the crosssection and on a approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme for all variation of section, even discontinuous with arbitrary large jumps. To do so, we introduce in the first step of the relaxation solver a singular dissipation measure superposed on the standing wave which enables us to control the approximate speeds of sound and thus, the time step, even for extreme initial data. Key-words : Discontinuous nozzle flows, relaxation techniques, Riemann problem. AMS subject classifications : 76S05, 35L60, 35F55.