By introducing the harmonic averaging point, we propose a new cell-centered finite volume scheme for evolutionary diffusion equation in this paper. On a mesh edge, we choose its two vertices and a harmonic averaging point as the auxiliary interpolation points. To make the finite volume scheme a cell-centered one, we replace the unknowns on these auxiliary points by the unknowns on the central point of the corresponding grid elements. Our scheme is linearity-preserving and local conservative, it can be applied on an arbitrary polygonal mesh. Considering the cases that the diffusion coefficient is continuous, discontinuous and nonlinear, respectively, four numerical experiments are implemented on six different polygonal meshes. The numerical results show that our scheme is second-order convergent in norm, it maintains good robustness for different types of diffusion coefficients, besides, it is easy to extend to 3D cases in programming.
Key words
finite volume method /
evolutionary diffusion equation /
arbitrary polygon mesh /
linearity-preserving /
harmonic averaging point
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References
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Footnotes
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