Hierarchical multi-dimensional limiting process on correction via reconstruction for compressible Euler equations

Abstract

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP) onto correction procedure via reconstruction (CPR). MLP, which has been originally developed in finite volume method (FVM), provides an accurate, robust and efficient oscillation-control mechanism in multiple dimensions for linear reconstruction. Recently, MLP has been extended into higher-order higher-order reconstruction. The proposed method, called hierarchical MLP, is developed in discontinuous Galerkin method, and it can be readily extended to CPR framework for solving compressible Euler equations. Through extensive numerical experiments, it is observed that that the proposed approach yields outstanding performances in resolving non-compressive as well as compressive flow features.