A fast flux-splitting for all speed flow

Abstract

A new flux spitting scheme capable of handling flow from incompressible to supersonic speeds has been developed in this paper. It is well known that there is a large disparity between the speed of acoustic waves and the speed of convective waves as the flow Mach number approaches zero. As a result, conventional flux-splitting methods such as Roe, van Leer, Osher and AUSM splittings all suffer in accuracy and stability in the incompressible flow limit. As a matter fact, singularities exist in all the above flux splitting methods when M ⇒ 0. In this study, a “representative” sound speed (RSS) is defined for flow with Mach number smaller than a threshold (e.g. 0.3) including the incompressible flow regime. Flux splitting is then based on the RSS instead of the true sound speed, eliminating the singularities. Another key ingredient is the pressure-velocity coupling provided by the present flux splitting which is crucial in the low speed flow regime. Several test cases are presented to demonstrate the capability of the new flux splitting method.