A new Roe-type scheme for all speeds

The all-speed Roe schemes still encounter the problem that the original Roe scheme does at high speeds because they are just improved in terms of low speeds. To overcome this problem, we propose a new scheme called RoeMAS (Roe Modified for All Speeds) in this paper. It changes the original Roe scheme's coefficients D^P and D^ρU to the order of O(c^-1) and O(c⁰) to improve the level of accuracy at low speeds. To be robust against the shock anomaly and the expansion shock at high speeds, it controls the coefficients of the density perturbation in the numerical mass flux instead of controlling those of the pressure perturbation like the RoeM-type schemes. Moreover, it changes the non-linear wave speeds in rarefactions' simulations to avoid using an entropy fix which is not satisfied in engineering area. Various numerical tests show that RoeMAS satisfies the following attractive properties independent of any tuning coefficient: (1) robustness against the shock anomaly and high discontinuity's resolution (2) free from the expansion shock's appearance (3) low dissipation and high resolution at low speeds. These properties suggest that RoeMAS is promising to be widely used to simulate flows of all speeds accurately and efficiently.