Properties of high-order FR/CPR method with subcell limiting in simulating flows around a circular half-cylinder

High-order CPR (Correction Procedure via Reconstruction) method has difficulties in treating strong shocks. Recently, Zhu et al. proposed a subcell CNNW (Compact Nonuniform Nonlinear Weighted) limiting strategy, which significantly enhances the shock-capturing capability of CPR. The CPR method with subcell limiting is in fact a hybrid scheme, employing high-order CPR in smooth regions and CNNW schemes in cells near discontinuities. The convergence and stability of the subcell CNNW scheme critically influence the performance of the hybrid CPR-CNNW scheme (abbreviated as HCCS). This study investigates the convergence and stability properties of the HCCS in simulating flows around circular half-cylinder. By comparing two limiters for the second-order CNNW scheme, we choose a better limiter for HCCS. Numerical tests on inviscid and viscous flows around circular half-cylinder demonstrate that the C2NNW2 scheme with the Venkatakrishnan limiter exhibits superiority in convergence and stability, thereby improving the overall numerical performance of the HCCS scheme.