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Highlights: [•] Multi-dimensional limiting strategy is extended in DG method for compressible flow. [•] Hierarchical MLP limiting strategy is developed for arbitrary DG-Pn reconstruction. [•] Extensive numerical validations are performed for inviscid and viscous flows. [•] DG-MLP method yields outstanding performance in resolving complex flow features. [Copyright &y& Elsevier]

Abstract: This paper deals with a robust, accurate and efficient multi-dimensional limiting strategy on three-dimensional unstructured grids within the framework of finite volume method. The present limiting strategy is on the line of continuous efforts to extend the multi-dimensional limiting process (MLP) onto three-dimensional tetrahedral grids, which was originally proposed on structured and triangular grids. In previous works, it was observed that the MLP limiting shows several superior characteristics, such as efficient control of multi-dimensional oscillations and accurate capture of both discontinuous and continuous multi-dimensional flow features, on triangular as well as structured grids. The design principle of the MLP limiters is based on the multi-dimensional limiting condition and the maximum principle, which can ensure multi-dimensional monotonicity through the global/local L ∞ stability. Consequently, it can be shown that the MLP limiting does satisfy the local extremum diminishing (LED) condition in a truly multi-dimensional way. The present MLP slope limiters are formulated into the setting of the three-dimensional Euler system, and are refined to improve convergence characteristics for steady state problems without compromising the accuracy of computed results. Through various numerical analyses and computations, it is demonstrated that the proposed MLP limiters provide the same level of successful performances previously observed on triangular and structured grids. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]