Numerical solutions to shock reflection and shock interaction problems for the self-similar transonic two-dimensional nonlinear wave systems

Abstract

We discuss numerical results for two dimensional Riemann problems for the nonlinear wave system. We consider four sectorial Riemann data and present the numerical results for two configurations. The first configuration is that incident shocks create reflected shocks, and the state behind the reflected shocks becomes subsonic. The second configuration is an interaction between two transonic shocks; one is created by an interaction with the sonic circle, and the other is created by the shock reflection. We implement Lax–Liu positive schemes and Strang splitting, and obtain linear correlations of the incident shock strength and the reflected shock strength for the first configuration. Furthermore we present intriguing numerical results on interactions of two transonic shocks for the second configuration.