A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids
Numerical Analysis
2019-01-08 v2
Abstract
The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchm\"{u}ller 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..
Keywords
Cite
@article{arxiv.1809.09355,
title = {A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids},
author = {Yulong Du and Li Yuan* and Yahui Wang},
journal= {arXiv preprint arXiv:1809.09355},
year = {2019}
}
Comments
9 tables, 3 figures