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

✍ Scribed by Felix Rieper

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 915 KB
• Volume: 229
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2009.09.043

✦ Synopsis

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.