Riemann problem in non-ideal gas dynamics

Abstract

In this paper we consider the Riemann problem for gas dynamic equations governing a one dimensional flow of van der Waals gases. The existence and uniqueness of shocks, contact discontinuities, simple wave solutions are discussed using R-H conditions and Lax conditions. The explicit form of solutions for shocks, contact discontinuities and simple waves are derived. The effects of van der Waals parameter on the shock and simple waves are studied. A condition is derived on the initial data for the existence of a solution to the Riemann problem. Moreover, a necessary and sufficient condition is derived on the initial data which gives the information about the existence of a shock wave or a simple wave for a 1-family and a 3-family of characteristics in the solution of the Riemann problem.