Efficient and Accurate Limiting Strategy for Discontinuous Galerkin Methods on Triangular and Tetrahedral Meshes

Abstract

The present paper deals with the robust, accurate and efficient limiting strategy for discontinuous Galerkin methods for high speed compressible flow. The present limiting strategy is a continuous work of extending multi-dimensional limiting process (MLP), which has been successful in finite volume methods (FVM), into discontinuous Galerkin (DG) methods on triangular and tetrahedral meshes. Based on successful analyses and implementations of the MLP slope limiting in FVM, MLP is applicable into DG framework with the MLP-based troubled-cell marker and the MLP slope limiter. It is observed that the proposed approach yields outstanding performances in resolving non-compressive as well as compressive flow features.