Riemann solution for one dimensional non-ideal isentropic magnetogasdynamics

Abstract

In the present paper, we study the Riemann problem for quasilinear hyperbolic system of partial differential equations governing the one dimensional non-ideal isentropic magnetogasdynamics with transverse magnetic field. We discuss the properties of rarefaction waves, shocks and contact discontinuities. Differently from single equation methods rooted in the ideal gasdynamics, the new approach is based on the system of two nonlinear algebraic equations imposing the equality of total pressure and velocity, assuming as unknowns the two values of densities, on both sides of the contact discontinuity. Newton iterative method is used to obtain densities. The resulting exact solver is implemented with the examples of general applicability of the proposed approach.