Year: 2019
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 768–784
Abstract
The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchmüller and Helzel can retain the full order of accuracy of the one-dimensional WENO reconstruction and requires only one flux computation per interface. The high-order accurate conversion between face-averaged values and face-center point values is the main ingredient of this method. In this paper, we derive sixth-order accurate conversion formulas on three-dimensional Cartesian grids. It is shown that the resulting modified FV WENO method is efficient and high-order accurate when applied to smooth nonlinear multidimensional problems, and is robust for calculating non-smooth nonlinear problems with strong shocks.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0254
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 768–784
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Finite volume method high-order accuracy dimension-by-dimension reconstruction Cartesian grid.