Development of a carbuncle-free and low-dissipation Roe-type scheme: Applications to multidimensional Euler flows

Abstract

The Roe scheme is known to have high resolution but to be afflicted by the notorious shock anomalies (such as the carbuncle phenomena) and the unphysical expansion shocks. This paper aims to develop a new Roe-type scheme which is robust for strong shock waves and low dissipative for contact waves and shear layers. Based on the mechanism analysis of shock instability, a dissipation-controlling strategy is adopted to adjust the entropy wave viscosity and shear wave viscosity of the transverse numerical flux in the numerical shock layer and the robustness of the Roe scheme is thus enhanced. The violation of entropy condition and the problem of expansion shocks are also fixed to broaden the scheme’s application scope. In addition, the THINC reconstruction procedure and a BVD algorithm are implemented to further improve the resolution for contact waves and shear layers. Numerical results of a series of classical one-, two- and three-dimensional test problems fully demonstrate that the proposed new Roe-type scheme has not only better robustness for strong shock waves but also higher resolution for contact waves and shear layers than the original Roe scheme.