Higher-order multi-dimensional limiting process for DG and FR/CPR methods on tetrahedral meshes

The present paper deals with the robust and accurate multi-dimensional limiting process for higher-order discontinuous Galerkin (DG) and flux resconstruction or correction procedure via reconstruction (FR/CPR) methods on tetrahedral meshes. 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 approximation. This limiting philosophy can be hierarchically extended into higher-order Pn approximation. The resulting algorithm has been developed for both DG and FR/CPR methods mostly on two-dimensional triangular meshes. This method can be efficiently extended and implemented into three-dimensional tetrahedral meshes. Through extensive numerical computations and comparisons, it is demonstrated that the proposed limiting approach yields the required order-of-accuracy and outstanding performances in resolving three-dimensional compressible inviscid and viscous flow features.