A priori subcell limiting approach for the FR/CPR method on unstructured meshes

TL;DR

This paper introduces an a priori subcell limiting method for high-order flux reconstruction on unstructured quadrilateral meshes, improving shock-capturing robustness by combining troubled cell detection with a finite difference scheme.

Contribution

It develops a novel subcell limiting approach with a modal energy indicator and a hybrid scheme for high-order methods on unstructured meshes.

Findings

Robust shock-capturing demonstrated on unstructured quadrilateral meshes.

Effective troubled cell detection using modal energy coefficients.

Enhanced stability of high-order flux reconstruction methods.

Abstract

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to calculate troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.