一种改进的Roe格式及其稳定性分析

Abstract

Low dissipation shock-capturing methods, including the popular Roe scheme, will encounter the shock instability phenomenon in the computation of the multidimensional strong shock wave problems. This will seriously affect the schemes’ accurate simulation of the hypersonic flow problems. The small perturbation analysis of the Roe scheme was carried out. The results show that, all perturbations in the longitudinal direction of the shock front are damped, but the perturbations of density and shear velocity in the transverse direction are undamped. The viscosities corresponding to the entropy wave and shear wave were added to the flux transverse to the shock front to suppress instability of the Roe scheme. To prevent the improper viscosity from influencing the resolution of contact discontinuity and shear layers, 2 switching functions were defined, so that the viscosity was only added to the transverse flux in the subsonic region of the shock layer. The numerical tests show that, the modified Roe scheme not only retains the merit of high resolution of the original Roe scheme, but also has better robustness and eliminates the shock wave instability.