@Article{CiCP-26-768, author = {}, title = {A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0254}, url = {http://global-sci.org/intro/article_detail/cicp/13146.html} }