Reduced dissipation AUSM-family fluxes: HR-SLAU2 and HR-AUSM+-up for high resolution unsteady flow simulations

The reduced dissipation approach is applied to AUSM-family flux functions of SLAU2 (as well as its predecessor, SLAU) and AUSM+-up for high resolution simulations. In this approach, a dominant dissipation term (of the pressure flux) in each flux function is locally controlled (0 < γHR < 1, γHR: dissipation coefficient) if a cell geometry is of high quality (i.e., fully or nearly rectangular) and flow is smooth, and the original method is recovered otherwise (γHR = 1). Numerical tests demonstrate that the proposed HR (High-Resolution, or Hi-Res) -SLAU2 achieves better resolution (while maintaining robustness) for a wide-ranging Mach numbers (from Mach 6 × 10−4 to 8.1), compared with the original counterparts (γHR = 1) or an existing method (HR-Roe), whereas HR-AUSM+-up shows degraded resolution due to a large cutoff Mach number at low speeds and insufficient dissipation at super- and hypersonic speeds, although a smaller γHR is allowed. Furthermore, a new wiggle detector is proposed to improve both convergence and solution accuracy.