Exact Riemann problem solutions and upwind fluxes for nonlinear elasticity

Abstract The present paper is devoted to the construction and comparative study of upwind methods as applied to the system of one-dimensional nonlinear elasticity equations. We derive a simple approach for building up exact solutions to the Riemann problem and construct a suite of test problems to assess numerical methods. Then we carry out the implementation and a systematic comparative study of some recently proposed simple, upwind fluxes, the focus being on robustness and accurate resolution of delicate features such as linearly degenerate fields.