The Compact and Accuracy Preserving Limiter for High-Order Finite Volume Schemes Solving Compressible Flows

In this paper, a new limiter namely the compact weighted biased average procedure (CWBAP) is proposed for the shock capturing of high-order finite volume methods on unstructured girds. The new feature of this limiter is that all its operations are based on the information within a compact stencil. This limiter is an improvement of the original weighted biased average procedure (WBAP) which is not compact due to its successive limiting feature when applied to high-order schemes. This improvement mainly relies on two new techniques: a successive secondary reconstruction and a two-step WBAP limiter. The new limiter can preserve the original order of accuracy of the high-order finite volume schemes when simulating smooth flow without shock waves, and it shows improvements in accuracy, resolution and convergence property over the original WBAP limiter according to the numerical results of a number of test cases. Furthermore, the compactness of this limiter reduces the amount of data transfer in parallel computing. When implemented into the newly developed high-order finite volume schemes based on the compact stencil, the efficiency of the parallel computing can be effectively improved.