A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids (Communications in Computational Physics, 2017)
This paper proposes a novel distance derivative weighted ENO (DDWENO)limiter based on fixed reconstruction stencil and applies it to the second- and high-orderfinite volume method on unstructured grids. We choose the standard deviationcoefficients of the flow variables as the smooth indicators by using the k-exact reconstructionmethod, and obtain the limited derivatives of the flow variables by weightingall derivatives of each cell according to smoothness. Furthermore, an additionalweighting coefficient related to distance is introduced to emphasize the contributionof the central cell in smooth regions. The developed limiter, combining the advantagesof the slope limiters and WENO-type limiters, can achieve the similar effect of WENOschemes in the fixed stencil with high computational efficiency. The numerical casesdemonstrate that the DDWENO limiter can preserve the numerical accuracy in smoothregions, and capture the shock waves clearly and steeply as well.