Volume 21, Issue 1
Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes

Xiang Lai, Zhiqiang Sheng & Guangwei Yuan

Commun. Comput. Phys., 21 (2017), pp. 162-181.

Published online: 2018-04

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  • Abstract

We construct a nonlinear monotone finite volume scheme for three-dimensional diffusion equation on tetrahedral meshes. Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme, we present a new efficient eliminating method. The scheme has only cell-centered unknowns and can deal with discontinuous or tensor diffusion coefficient problems on distorted meshes rigorously. The numerical results illustrate that the resulting scheme can preserve positivity on distorted tetrahedral meshes, and also show that our scheme appears to be approximate second-order accuracy for solution.

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@Article{CiCP-21-162, author = {}, title = {Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {162--181}, abstract = {

We construct a nonlinear monotone finite volume scheme for three-dimensional diffusion equation on tetrahedral meshes. Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme, we present a new efficient eliminating method. The scheme has only cell-centered unknowns and can deal with discontinuous or tensor diffusion coefficient problems on distorted meshes rigorously. The numerical results illustrate that the resulting scheme can preserve positivity on distorted tetrahedral meshes, and also show that our scheme appears to be approximate second-order accuracy for solution.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220415.090516a}, url = {http://global-sci.org/intro/article_detail/cicp/11236.html} }
TY - JOUR T1 - Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes JO - Communications in Computational Physics VL - 1 SP - 162 EP - 181 PY - 2018 DA - 2018/04 SN - 21 DO - http://dor.org/10.4208/cicp.220415.090516a UR - https://global-sci.org/intro/article_detail/cicp/11236.html KW - AB -

We construct a nonlinear monotone finite volume scheme for three-dimensional diffusion equation on tetrahedral meshes. Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme, we present a new efficient eliminating method. The scheme has only cell-centered unknowns and can deal with discontinuous or tensor diffusion coefficient problems on distorted meshes rigorously. The numerical results illustrate that the resulting scheme can preserve positivity on distorted tetrahedral meshes, and also show that our scheme appears to be approximate second-order accuracy for solution.

Xiang Lai, Zhiqiang Sheng & Guangwei Yuan. (2020). Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes. Communications in Computational Physics. 21 (1). 162-181. doi:10.4208/cicp.220415.090516a
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