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

Xiang Lai ,  Zhiqiang Sheng and Guangwei Yuan

10.4208/cicp.220415.090516a

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

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  • Abstract

We construct a nonlinear monotone finite volume scheme for threedimensional 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.

  • History

Published online: 2018-04

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