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

Yulong Du, Li Yuan & Yahui Wang

DOI: 10.4208/cicp.OA-2018-0254

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 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.

  • 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 = {Yulong Du, Li Yuan and Yahui Wang}, 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} }
TY - JOUR T1 - A High-Order Modified Finite Volume WENO Method on 3D Cartesian Grids AU - Yulong Du, Li Yuan & Yahui Wang JO - Communications in Computational Physics VL - 3 SP - 768 EP - 784 PY - 2019 DA - 2019/04 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0254 UR - https://global-sci.org/intro/article_detail/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 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.

Yulong Du, Li Yuan and 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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