Volume 18, Issue 3
A Finite Volume Scheme for Three-Dimensional Diffusion Equations

Xiang Lai, Zhiqiang Sheng & Guangwei Yuan

Commun. Comput. Phys., 18 (2015), pp. 650-672.

Published online: 2018-04

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  • Abstract

The extension of diamond scheme for diffusion equation to three dimensions is presented. The discrete normal flux is constructed by a linear combination of the directional flux along the line connecting cell-centers and the tangent flux along the cell-faces. In addition, it treats material discontinuities by a new iterative method. The stability and first-order convergence of the method are proved on distorted meshes. The numerical results illustrate that the method appears to be approximate second-order accuracy for solution.

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@Article{CiCP-18-650, author = {}, title = {A Finite Volume Scheme for Three-Dimensional Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {3}, pages = {650--672}, abstract = {

The extension of diamond scheme for diffusion equation to three dimensions is presented. The discrete normal flux is constructed by a linear combination of the directional flux along the line connecting cell-centers and the tangent flux along the cell-faces. In addition, it treats material discontinuities by a new iterative method. The stability and first-order convergence of the method are proved on distorted meshes. The numerical results illustrate that the method appears to be approximate second-order accuracy for solution.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.140813.230215a}, url = {http://global-sci.org/intro/article_detail/cicp/11044.html} }
TY - JOUR T1 - A Finite Volume Scheme for Three-Dimensional Diffusion Equations JO - Communications in Computational Physics VL - 3 SP - 650 EP - 672 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.140813.230215a UR - https://global-sci.org/intro/article_detail/cicp/11044.html KW - AB -

The extension of diamond scheme for diffusion equation to three dimensions is presented. The discrete normal flux is constructed by a linear combination of the directional flux along the line connecting cell-centers and the tangent flux along the cell-faces. In addition, it treats material discontinuities by a new iterative method. The stability and first-order convergence of the method are proved on distorted meshes. The numerical results illustrate that the method appears to be approximate second-order accuracy for solution.

Xiang Lai, Zhiqiang Sheng & Guangwei Yuan. (2020). A Finite Volume Scheme for Three-Dimensional Diffusion Equations. Communications in Computational Physics. 18 (3). 650-672. doi:10.4208/cicp.140813.230215a
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