A hierarchical reconstruction for DG/FV method with low dispersion: Basic formulation and applications

Journal article, 2021

In this paper, the numerical dispersion of a hierarchical reconstruction strategy for DG/FV method has been optimized. For the hierarchical strategy, the cell averages and the first derivatives are reconstructed based on the Hermite WENO method; the second derivatives are reconstructed via Green-Gauss integration and WENO reconstruction. Then, the numerical dispersion has been optimized by minimizing error with bandwidth optimization technique. Furthermore, to adjust the loss of compactness due to the reconstructed second derivatives, two modifications were also proposed with optimal weights. Eventually, from the implementations in scalar and compressible Euler equations, the superiority of numerical dispersion and accuracy of present methods could be validated. The shock capturing capacity has also been validated in 1D and 2D cases.