Multi-Dimensional Limiting Strategy for Arbitrary Higher-Order Discontinuous Galerkin Methods in Inviscid and Viscous Flows

Abstract

The present paper deals with the multi-dimensional limiting process (MLP) for arbitrary higher-order discontinuous Galerkin (DG) methods to compute compressible inviscid and viscous flows. MLP, which has been quite successful in finite volume methods (FVM), is extended into DG methods for hyperbolic conservation laws. We firstly formulate the robust and accurate hierarchical MLP limiting strategy for DG-P n(n 2) reconstruction. Secondly, the resulting method, called the DG-MLP method, is applied to various inviscid and viscous flows. In the final paper, detailed numerical procedure for the hierarchical DG-MLP formulation and extensive numerical test cases to demonstrate its numerical accuracy and robustness will be given.