The p-Weighted Limiter for the Discontinuous Galerkin Method in Solving Compressible Flows on Tetrahedral Grids

Abstract

This paper makes several improvements to generalise the p-weighted limiter for the discontinuous Galerkin (DG) method proposed in 1D and triangular grids [Li, Wanai, Qian Wang, and Yu Xin Ren. 2020. “A P-weighted Limiter for the Discontinuous Galerkin Method on One-dimensional and Two-dimensional Triangular Grids.” Journal of Computational Physics 407: 109246] to tetrahedral grids for solving compressible flows. First, the limiter would be performed using the local coordinates instead of the physical coordinates, which coincides with the DG solution and saves the expensive cost in transforming the solution to the physical space. Second, the weighted procedure in the local coordinates can be more efficient by storing some cell-independent constants. Third, the parameter, which prevents very large weights on the linear candidate polynomials at extrema, is replaced by a formula to meet the requirement of ϵ. These improvements construct an efficient way in calculating compressible flows in complex geometries. Inviscid and viscous tests are calculated to validate the shock capturing capability of the limiter and the high-order accuracy of the DG schemes.