Two-dimensional Riemann problem involving three J’s for a hyperbolic system of nonlinear conservation laws

Abstract

In this paper, we study the Riemann problem for a two-dimensional hyperbolic system of conservation laws with initial data projecting exactly three contact discontinuities. We use the generalized characteristic analysis method to analyze interactions of contact discontinuities, and obtain six analytical solutions and corresponding criteria. Delta shock waves and spiral structures appear in some solutions. We also conduct numerical experiments, and numerical results confirm the geometric structures of the constructed solutions.