Multi-dimensional limiting strategy for arbitrary higher-order discontinuous galerkin methods in inviscid and viscous flows

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. From the previous works, it was observed that the MLP methods provide an accurate, robust and efficient oscillation-control mechanism in multiple dimensions for linear reconstruction. This limiting philosophy can be extended into higherorder reconstruction. The proposed algorithm, called the hierarchical MLP, facilitates the accurate capturing of detailed flow structures in both continuous and discontinuous regions. Through extensive numerical analyses and computations on triangular and tetrahedral grids, it is demonstrated that the proposed limiting approach yields the desired accuracy and outstanding performances in resolving compressible inviscid and viscous flow features.