A Uniform Algorithm for All-Speed Shock-Capturing Schemes

Abstract

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.

References in corpus (1)

• Mechanism and Improvement of the Harten-Lax-van Leer Scheme for All-Speed Flows

Cited by in corpus (4)

• On the All-Speed Roe-type Scheme for Large Eddy Simulation of Homogeneous Decaying Turbulence
• An Improved Roe Scheme for All Mach-Number Flows Simultaneously Curing Known Problems
• The Role of Momentum Interpolation Mechanism of the Roe Scheme in the Shock Instability
• Cures for the Expansion Shock and the Shock Instability of the Roe Scheme