The influence of cell geometry on the accuracy of upwind schemes in the low mach number regime

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, presented in this paper, is the dependence on the cell geometry: applied on a triangular grid, the accuracy problem disappears, i.e. flows of arbitrarily small Mach numbers can be simulated on a fixed mesh. We give an asymptotic analysis of this, up to date unknown, phenomenon for the first-order Roe scheme and present a number of numerical results.