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.

• Periodical: Applied Mechanics and Materials (Volume 872)
• Pages: 393-398
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.872.393
• Online since: October 2017
• Authors: Wei Zhang*, Jin Song Bai, De Jun Sun
• Keywords: HLLD, Non-Linear Elasticity, Ppm, Riemann Solver

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