On two-dimensional Riemann problem for pressure-gradient equations of the Euler system

Abstract

We consider the two-dimensional Riemann problem for the pressure-gradient equations with four pieces of initial data, so restricted that only one elementary wave appears at each interface. This model comes from the flux-splitting of the compressible Euler system. Lack of the velocity in the eigenvalues, the slip lines have little influence on the structures of solutions. The flow exhibits the simpler patterns than in the Euler system, which makes it possible to clarify the interaction of waves in two dimensions. The present paper is devoted to analyzing the structures of solutions and presenting numerical results to the two-dimensional Riemann problem. Especially, we give the criterion of transition from the regular reflection to the Mach reflection in the interaction of shocks.