A Godunov-Type Method to Euler Equations for Magnetogasdynamic in a Variable Cross-Section Duct

The present paper concerns with a Godunov-type method for the isentropic polytropic gas subjected to transverse magnetic field in a variable cross-section duct.Typical Riemann solutions are used to build the numerical flux at cell interface. We mainly address and solve numerically two special cases of the solution: one losses uniqueness and the other contains a resonance wave. Numerical simulations including both the Riemann problem and the flow in a de Laval nozzle in a large time are given, which show that the scheme is efficient and accurate. The expected order is achieved by convergence rate study