Accuracy in a Finite Volume Godunov Type Method

Abstract

The standard Godunov type method used in computational fluid dynamics shows accuracy problems for low Mach number flows and for the kinetic energy at the highest wave numbers resolvable on a given grid. Both drawbacks become visible when simulating the decay of isotropic turbulence at the low Mach numbers typical for the respective experimental investigations. A modification to cure both problems is proposed by Thornber et al. [10] with a mathematical motivation in case of a special fifth order reconstruction. The theoretical results are repeated here. Numerical results are achieved for schemes not investigated in that literature, namely AUSMDV and AUSM+-up which includes already modifications for low Mach number flows. First experiences with Thornber’s modification confirm the positive influence in combination with AUSMDV even if the reconstruction is only of second order. In combination with AUSM+-up Thornber’s modification provides too little damping.