Comparative Study of Shock-Capturing Methods for High-Order CPR: MLP and Artificial Viscosity

The present paper compares the two shock-capturing approaches for higher-order correction procedure via reconstruction (CPR) method; artificial viscosity and multi-dimensional limiting process (MLP). MLP, which has been a successful solution limiting method in finite volume method, is recently extended to higher-order DG and CPR methods in a hierarchical manner. By properly limiting multi-dimensional solutions, it efficiently suppresses spurious oscillations around multi-dimensional shock discontinuity while keeping the solution accuracy in smooth region. At the same time, the localized artificial viscosity method (LAV) provides a robust damping mechanism around shock waves and resolves complex flow structure accurately. Both methods have their own merits but there is a room for further improvement to unveil the physics of complex compressible flows. By comparing them in terms of robustness, accuracy and efficiency, further issues to develop the optimal shock-capturing algorithms are discussed