On New Simple Low-Dissipation Scheme of AUSM-Family for All Speeds

Abstract

Compressible CFD methods for all speeds that can compute very low Mach number flows with low dissipation, as well as strong shock and expansion waves in high Mach number flows, are very attractive for aerospace applications such as sound generation by supersonic plume, flows in a rocket engine combustor, and cavitating gas-liquid flows. We present here such a new simple numerical flux of AUSM-family for all speeds with no tunable parameters, named SLAU (Simple Low-dissipation AUSM), along with its formulation. This scheme features low dissipation in low Mach number regime, while keeping robustness and non-oscillating nature at high Mach numbers, i.e., stabilities against shock-induced anomalies such as the carbuncle phenomenon. Furthermore, although this method does not use nor rely on scaling of numerical viscosity by the preconditioning matrix, its combination with the time derivative preconditioning is proved to be quite effective for fast convergence in low Mach number flows. These advantages of the present scheme will be demonstrated in applications to flow computations of wide-ranging Mach numbers.