Exact and Approximate Riemann Solvers for Real Gases

Abstract

A procedure is developed for solving the Riemann problem (RP) for the flow of gases obeying an equation of state (EOS) of the form p = p (ρ, τ). A first method is introduced, producing solutions of the exact RP; the algorithm is validated by applying it to the classical test case of the shock-tube, for a perfect gas. Thereafter, the method is applied to gases having EOS of the Van der Waals or virial types, with very good resulting accuracy; however, the procedure is somewhat demanding in computer time. Therefore, some simplifying assumptions are introduced into the computation of simple waves, leading to an approximate solution of the RP; in most circumstances, excellent results are obtained, and the computer time is much more competitive. However, under certain extreme flow conditions, it is recommended that a combination of the exact and approximate solvers for the RP be employed.