Accurate and Robust Hybrid HLLC Riemann Solver on Triangular Grids

Abstract

The HLLC scheme is an accurate, approximate Riemann solver. However, it suffers from the carbuncle phenomenon and numerical shock instability problems on both rectangular and triangular grids. In this paper, a hybrid HLLC scheme ([Formula: see text]) is developed by adding some extra computations to the original HLLC scheme in order to achieve a stable and accurate scheme. The idea of the hybrid scheme is straightforward as it uses a simple shock-capturing function with parameter [Formula: see text] to detect regions where pressure oscillations such as shock waves are significant. In these regions, a less diffusive version of the [Formula: see text] scheme ([Formula: see text]) is activated with a new weighting function with parameter [Formula: see text]. This new weighting function is designed to control the stability and accuracy of the hybrid scheme via the ratio of the square of the speed of sound of two adjacent cells. A linear perturbation analysis of an odd–even decoupling problem is used to analyze the effectiveness of the proposed hybrid scheme in damping perturbations. Several numerical examples are given to demonstrate that the new scheme ([Formula: see text]) can obtain accurate solutions and that it is simple and efficient and requires comparable computational time with the original scheme.