AUFSR+: Low Mach number enhancement of the AUFSR scheme

A low-Mach number extension of the low-diffusion AUFSR scheme, called AUFSR+, is proposed. The extension is facilitated by a simple scaling of the normal velocity jump across the cell interface, applied on the AUFSR artificial dissipation part. The scaling is based on a simple function of the Mach number that is free from any global cut-off reference velocity. Moreover, a shock sensor is introduced into the Mach number function to avoid possible numerical instabilities near shocks, such that the AUFSR+ scheme returns to the original AUFSR scheme. The modified scheme has been implemented within a flow solver and is used in this paper to compute a variety of inviscid and viscous flow problems in two- and three-dimensions. Numerical results that are obtained indicate that the new scheme is attractive across a wide range of Mach numbers, in terms of accuracy and robustness.