A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids

Abstract

AbstractThis paper proposes a novel distance derivative weighted ENO (DDWENO) limiter based on fixed reconstruction stencil and applies it to the second- and highorder finite volume method on unstructured grids. We choose the standard deviation coefficients of the flow variables as the smooth indicators by using the k-exact reconstruction method, and obtain the limited derivatives of the flow variables by weighting all derivatives of each cell according to smoothness. Furthermore, an additional weighting coefficient related to distance is introduced to emphasize the contribution of the central cell in smooth regions. The developed limiter, combining the advantages of the slope limiters and WENO-type limiters, can achieve the similar effect of WENO schemes in the fixed stencil with high computational efficiency. The numerical cases demonstrate that the DDWENO limiter can preserve the numerical accuracy in smooth regions, and capture the shock waves clearly and steeply as well.