A Multi-State HLL Approximate Riemann Solver for Solid/Vacuum Riemann Problem

Abstract

A new multi-state HLLD (‘‘D’’ stands for Discontinuities.) approximate Riemann solver for Riemann problem of nonlinear elastic solid is developed based on the assumption that a wave configuration for the solution that consists of five waves (two slow waves, two fast waves and a contact discontinuity) separating six constant states. Since the intermediate states satisfied with the Rankine-Hugoniot relations in this approximate Riemann system are analytically obtained, the HLLD Riemann solver can be constructed straightforwardly. The Piecewise Parabolic Method (PPM) is used directly to construct high-order finite-volume schemes. Numerical tests demonstrate that the scheme PPM coupled with HLLD is robust and efficient. It indicates that the scheme PPM+ HLLD can be useful in practical applications for the non-linear elasticity.