Multidimensional Riemann problem with self-similar internal structure. Part II - Application to hyperbolic conservation laws on unstructured meshes

The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we consider the Euler equations of compressible gas dynamics as well as the equations of ideal magnetohydrodynamics (MHD). Several stringent test problems are solved for both PDE systems.