Assessment of riemann solvers for unsteady one-dimensional inviscid flows of perfect gases

The solution of Riemann problems for the one-dimensional Euler equations with polytropic gases usually involves a numerical iterative solution procedure, and more efficient Riemann solvers can reduce computational times and costs by factors of up to 25, Riemann solvers that have been used in past computational fluid dynamics, those that are used in current numerical work, and a new and more efficient one reported in this paper are all assessed in terms of their relative computational performance. This assessment includes the type of shock and rarefaction-wave equations, iterative procedures, and initial guesses used by Godunov, Chorin, Van Leer, Smoller, and others. Various aspects of the Riemann problem and its solution for unsteady flows are also discussed in terms of the pressure-velocity diagram, both for completeness and to add some new practical insights for improving computer codes.