A parameter-free upwind scheme for all speeds’ simulations

With the rapid development of the computational fluid dynamics (CFD), a parameter-free upwind scheme capable of simulating all speeds accurately and efficiently is in high demand. To achieve this goal, we present a new upwind scheme called AUSMPWM in this paper. This scheme computes the numerical mass flux as the AUSMPW+ and computes the interfacial sound speed in a different way. Also, it computes the pressure flux by limiting the dissipation if the Mach number is less than 1. Series of numerical experiments show that AUSMPWM can satisfy the following attractive properties independent of any tuning coefficient: (1) Robustness against the shock anomaly and high discontinuity’s resolution; (2) high accuracy on hypersonic heating prediction and capability to give smooth reproductions of heating profiles; (3) low dissipation at low speeds; and (4) strong grid, reconstruction scheme, and Mach number independence in low speeds’ simulations. These properties suggest that AUSMPWM is promising to be widely used to accurately and efficiently simulate flows of all speeds.