On the dissipation mechanism of upwind-schemes in the low Mach number regime: A comparison between Roe and HLL

It is well known that standard upwind schemes for the Euler equations face a number of problems in the low Mach number regime: stiffness, cancellation and accuracy problems. A new aspect of the accuracy problem, presented in this paper, is the dependence on the type of flux solver: while the accuracy of the HLL scheme massively decreases for Ma → 0 on a given triangular mesh, the Roe scheme remains accurate, i.e. flows of arbitrarily small Mach numbers can – at least in principle – be simulated on a fixed triangular mesh. We give an asymptotic analysis of this phenomenon and present a number of numerical results.