An Effective AUSM-Type Scheme for Both Cases of Low Mach Number and High Mach Number

A new scheme called AUSMAS (Advection Upstream Splitting Method for All Speeds) is proposed for both high speed and low speed simulation cases. For the cases of low speed, it controls the checkerboard decoupling by keeping the coefficient of the pressure difference to the order of O(Ma⁻¹) in the mass flux. Furthermore, it is able to guarantee a high level of accuracy by keeping the coefficients of the dissipation terms to the order of O(Ma⁰) in the momentum flux. For the cases of high speeds, especially at supersonic and hypersonic speeds, it is able to avoid the appearance of the shock anomaly by controlling the coefficients of the density perturbation in the mass flux. AUSMAS is testified to have the following attractive properties according to various numerical tests: (1) robustness against the abnormal shock; (2) high resolution in discontinuity; (3) the appearance of the unphysical expansion shock is avoided; (4) high resolution and low dissipation at low speeds; (5) independent of any tuning coefficient. These properties determined that AUSMAS has great promise in efficiently and accurately simulating flows of all speeds.