Higher-order Multi-dimensional Limiting Strategy for Correction Procedure via Reconstruction

Abstract

Higher-order multi-dimensional limiting Process (MLP) [J. S. Park and C. Kim, Higher-order Multi-dimensional Limiting Strategy for Discontinuous Galerkin Methods in Compressible Inviscid and Viscous Flows, Comp. & Fluids, In press] is improved and applied to correction procedure via reconstruction (CPR) on unstructured grids. MLP, which has been originally developed in nite volume method (FVM), provides an accurate, robust and ecient oscillation-control mechanism in multiple dimensions for linear reconstruction. This limiting philosophy can be hierarchically extended into higher-order Pn reconstruction. The resulting algorithms, called the hierarchical MLP, facilitate the accurate capturing of detailed flow structures in both continuous and discontinuous regions. This algorithm has been developed in the modal DG framework, but it also can be formulated into a nodal framework, most notably the CPR framework. Troubled-cells are detected by applying the MLP concept, and the nal accuracy is determined by the projection procedure and MLP limiting step. Through extensive numerical analyses and computations, it is demonstrated that the proposed limiting approach yields the desired accuracy and outstanding performances in resolving compressible inviscid and viscous flow features.