A shock-stable rotated-hybrid Riemann solver on rectangular and triangular grids

Abstract

The rotated Riemann solver is robust against the carbuncle phenomenon, especially for multidimensional computation. Moreover, hybrid techniques are usually used to enhance the stability of an accurate scheme by combining an accurate scheme with a diffusive scheme. This paper proposes a rotated-hybrid Riemann solver named the rotated-HLLC+ scheme. The scheme is developed by hybridizing the Harten–Lax–van Leer contact (HLLC) scheme with the advection upstream splitting method based on a flux vector splitting (AUSMV+) scheme by following the rotated Riemann solver approach. The unit vector n1 is calculated from the velocity-difference vector, and the unit vector n2 is the orthogonal vector. The linearized analysis suggests that the HLLC scheme should be used in the direction of n1 and the AUSMV+ scheme in the direction n2. In this way, the hybrid scheme becomes shock-stable with less numerical dissipation. Moreover, the pressure-based method is used to detect the shock wave. Several numerical experiments suggest that the pressure cutoff parameter εp=0.01 may be generally suitable and provide a stable solution with little additional numerical dissipation. The last two numerical examples show that the computational performance of the rotated-HLLC+ scheme is comparable to the HLLC scheme for the weak shock reflection over convex double wedges. However, the scheme is approximately 9% faster than the HLLC scheme for the double Mach reflection of a strong shock wave. The proposed scheme gives fast, stable, and accurate solutions on rectangular and triangular grids.