Automatic Wave Curve Structure Detection for the Computation of Reference Solutions of Non-Classical Riemann Problems

This paper outlines a solver for the computation of exact solutions of non-classical Riemann problems for the 1D Euler equations of gas-dynamics. The rarefaction and compression wave curve structures are automatically detected by minimizing two cost functions that embed all relevant physical constraints. The presented solver is automated but expensive, and is not meant to be used for the computation of fluxes in a Godunov-type solver, but rather for the computation of reference solutions for the validation of numerical tools. Some sample Riemann problems with non-classical waves are presented.