Research on high-order flux reconstruction method with adaptive mesh for shock capturing

Abstract

High order schemes have been developed for a quite long time, and many famous schemes arise like Discontinuous Galerkin (DG), Spectral Difference (SD) and WENO schemes, etc. The Flux Reconstruction (FR) scheme proposed by Huynh has attracted the attention of researchers for its simplicity and efficiency. It’s written in differential form and bridges the DG and SD schemes, which can be constructed with a proper choice of parameter. In this paper, realize FR scheme based on the framework of the open source Adaptive Mesh Refinement (AMR) library p4est. To capture shock sharply, the performance of Localized Laplacian Artificial Viscosity (LLAV) and In-cell Piecewise Integrated Solution methods are compared. As an important way of reducing computational cost, AMR technique integrated in p4est is also combined with FR. The performance of the developed code is tested in both one dimensional and two dimensional and get some quite attracting results.