Uniform algorithm for all-speed shock-capturing schemes

Many ideas exist for the development of shock-capturing schemes, such as Roe, Harten–Lax–van Leer (HLL) and advection upstream splitting method (AUSM) families, and their extension for all-speed flow. A uniform algorithm that expresses the three families in the same framework is proposed in this study. The algorithm has an explicit physical meaning, provides new understanding and comparison of the mechanism of schemes, and may play a significant role in further research. As an example of applying the uniform algorithm, the low Mach number behaviour of the schemes is analysed. A clear and simple explanation is provided based on the wall boundary, and a concise rule is proposed to determine whether a scheme has satisfied low Mach number behaviour.