In numerical simulations of multidimensional high Mach flows, the conventional low-diffusion upwind schemes built on the dimensional splitting method will encounter the shock instability which is mainly manifested as the infamous carbuncle phenomena. A linear stability analysis reveals that the shock instability is triggered by the unattenuated perturbations in the transverse direction of the flow field. In the present work, an accurate and shock-stable genuinely multidimensional numerical scheme based on the Toro-Vázquez splitting method is p...
