Volume 26, Issue 3
A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids

Yulong Du, Li Yuan & Yahui Wang

Commun. Comput. Phys., 26 (2019), pp. 768-784.

Published online: 2019-04

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  • Abstract

The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchm ¨uller 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 highorder accurate when applied to smooth nonlinear multidimensional problems, and is robust for calculating non-smooth nonlinear problems with strong shocks.

  • Keywords

Finite volume method, high-order accuracy, dimension-by-dimension reconstruction, Cartesian grid.

  • AMS Subject Headings

65M08, 65M12, 65M20

  • Copyright

COPYRIGHT: © Global Science Press

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@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 Buchm ¨uller 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 highorder 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} }
TY - JOUR T1 - A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids JO - Communications in Computational Physics VL - 3 SP - 768 EP - 784 PY - 2019 DA - 2019/04 SN - 26 DO - http://dor.org/10.4208/cicp.OA-2018-0254 UR - https://global-sci.org/intro/cicp/13146.html KW - Finite volume method, high-order accuracy, dimension-by-dimension reconstruction, Cartesian grid. AB -

The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchm ¨uller 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 highorder accurate when applied to smooth nonlinear multidimensional problems, and is robust for calculating non-smooth nonlinear problems with strong shocks.

Yulong Du, Li Yuan & Yahui Wang. (2019). A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids. Communications in Computational Physics. 26 (3). 768-784. doi:10.4208/cicp.OA-2018-0254
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