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A Finite Volume Scheme for Three-Dimensional Diffusion Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  14 September 2015

Xiang Lai ,
Zhiqiang Sheng  and
Guangwei Yuan
Xiang Lai
Affiliation:
Department of Mathematics, Shandong University, Jinan 250100, P.R. China
Zhiqiang Sheng
Affiliation:
Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
Guangwei Yuan*
Affiliation:
Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
*
*Corresponding author. Email addresses: [email protected] (X. Lai), [email protected] (Z. Sheng), [email protected] (G. Yuan)
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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 is proved on distorted meshes. The numerical results illustrate that the method appears to be approximate second-order accuracy for solution.

Keywords

Finite volume schemediffusion equationtetrahedral meshes

MSC classification

Secondary: 65M08: Finite volume methods 65M12: Stability and convergence of numerical methods 65M55: Multigrid methods; domain decomposition
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 3 , September 2015 , pp. 650 - 672
Copyright
Copyright © Global-Science Press 2015 

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