Hierarchical Multi-dimensional Limiting Strategy on Dg Discretization for Compressible Navier-stokes Equations

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP) for higher-order discontinuous Galerkin (DG) methods to compute compressible Navier-Stokes equation. From the previous works, it was observed that the MLP shows several superior characteristics, such as efficient controlling of multi-dimensional oscillations and accurate capturing of complex flow structure. Recently, MLP has been extended into DG method for hyperbolic conservation laws. The proposed method, called hierarchical MLP, can be readily extended to convection-dominated problem, such as compressible Navier-Stokes equation. Through several test cases, it is observed that that the proposed approach yields outstanding performances in resolving non-compressive as well as compressive viscous flow features.