Troubled cell detection in subcell limiting for high-order CPR method on unstructured meshes

The correction procedure via reconstruction (CPR) method is an efficient and compact method, suitable for unstructured meshes, but it cannot solve the problem with strong discontinuities in flow fields. Based on the shock-capturing scheme with second-order non-uniform nonlinear weighted interpolation, we previously developed a subcell limiting technique for the high-order CPR method on two-dimensional unstructured quadrilateral meshes. Within this technique, the troubled cells are first divided into non-uniform subcells, then a second-order shock-capturing scheme is adopted for the calculation. As the solution points are overlaid between the main cells and the subcells, it is very convenient to handle the data exchange in the two layers. The detection of troubled cells is a crucial step in the subcell limiting technique, and the number and distribution of troubled cells can both affect the numerical results. Based on this, the present study considers two methods of troubled cell detecting, i.e. detecting by cell and detecting by dimension. This paper compares and analyzes the influence of different indicators, i.e. TVB, MDH, and JST, on the resolution of numerical schemes through typical benchmark cases such as the shock tube problem, the Shu-Osher problem, the double Mach reflection problem, and the shock-vortex interaction. The results show that detecting by dimension can reduce the number of troubled cells, thereby improving the resolution, which has a certain scientific value.