A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes (Communications in Computational Physics, 2022)
A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based onmodal energy coefficients is proposed to detect troubled cells, where discontinuitiesexist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing schemebased on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPRmethod. Numerical investigations show that the proposed subcell limiting strategy onunstructured quadrilateral meshes is robust in shock-capturing.
Keywords: Flux reconstruction/correction procedure via reconstruction; shock capturing; subcell limiting; unstructured meshes.