MULTIDIMENSIONAL DISSIPATION TECHNIQUE FOR AN AUSM SCHEME ON TRIANGULAR GRIDS

Numerical instability of the AUSM scheme on two-dimensional structured triangular grids is investigated. By examining several test cases, it is found that both numerical flux formulations of the AUSM scheme (so-called the AUSM-M1 and AUSM-M2 schemes) do not have sufficiently robustness to satisfy the shock-induced anomaly so called the carbuncle phenomenon. The modified multidimensional dissipation technique is then proposed in order to heal such shock instability. The dissipation mechanism against perturbations is investigated by applying a linearized discrete analysis to the odd-even decoupling problem. The recursive equations show that the dissipation factor (δ) plays an important role in all perturbations of the AUSM-M1 scheme. But it does not have any effect on the density perturbation of the AUSM-M2 scheme. Finally, the scheme is further extended to achieve the second-order solution accuracy and evaluated theirs robustness against shock instability by solving several test cases.