%0 Journal Article
%T A Uniform Algorithm for All-Speed Shock-Capturing Schemes
%A Xue-song Li
%J Physics
%D 2012
%I arXiv
%R 10.1080/10618562.2014.936315
%X There are many ideas for developing shock-capturing schemes and their extension for all-speed flow. The representatives of them are Roe, HLL and AUSM families. In this paper, a uniform algorithm is proposed, which expresses three families in the same framework. The algorithm has explicit physical meaning, provides a new angel of understanding and comparing the mechanism of schemes, and may play a great role in the further research. As an example of applying the uniform algorithm, the low-Mach number behaviour of the schemes is analyzed. Then, a very clear and simple explanation is given based on the wall boundary, and a concise rule is proposed to judge whether a scheme has satisfied low-Mach number behaviour.
%U http://arxiv.org/abs/1201.1553v2