Decomposition of the Wave Manifold into Lax Admissible Regions and its Application to the Solution of Riemann Problems

Abstract

We utilize a three-dimensional manifold to solve Riemann Problems that arise from a system of two conservation laws with quadratic flux functions. Points in this manifold represent potential shock waves, hence its name wave manifold. This manifold is subdivided into regions according to the Lax admissibility inequalities for shocks. Finally, we present solutions for the Riemann Problems for various cases and exhibit continuity relative to $L$ and $R$ data, despite the fact that the system is not strictly hyperbolic. The usage of this manifold regularizes the solutions despite the presence of an elliptic region.