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A Finite Volume Scheme for Three-Dimensional Diffusion Equations

Published online by Cambridge University Press:  14 September 2015

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: qxlai2000@sdu.edu.cn (X. Lai), sheng_zhiqiang@iapcm.ac.cn (Z. Sheng), yuan_guangwei@iapcm.ac.cn (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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

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