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Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes

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

Published online by Cambridge University Press:  05 December 2016

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 Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R.China
Guangwei Yuan*
Affiliation:
Laboratory of 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)
*Corresponding author. Email addresses:qxlai2000@sdu.edu.cn (X. Lai), sheng_zhiqiang@iapcm.ac.cn (Z. Sheng), yuan_guangwei@iapcm.ac.cn (G. Yuan)
*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

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.

Keywords

Monotonicityfinite volume schemediffusion equationtetrahedral meshes

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 65M55: Multigrid methods; domain decomposition
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017 , pp. 162 - 181
Copyright
Copyright © Global-Science Press 2016 

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