An improved monotone finite volume scheme for diffusion equation on polygonal meshes
An improved monotone finite volume scheme for diffusion equation on polygonal meshes
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DOI：
10.1016/j.jcp.2012.01.015
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
Z. Sheng;G. Yuan
中科院分区：
文献类型：
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作者：
Z. Sheng;G. Yuan
在多边形网格上构造了扩散方程的一个新的非线性单调有限体积格式。新格式采用单元边未知数代替单元顶点未知数作为辅助未知数，提高了单调格式的精度。我们的计划是局部保守的，只有细胞为中心的未知数。数值结果表明，我们的计划是如何保持积极的各种扭曲的网格。数值结果表明，新格式具有较强的鲁棒性，在某些网格上比现有的单调格式精度更高。
We construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes. The new scheme uses the cell-edge unknowns instead of cell-vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes. Specially, numerical results show that the new scheme is robust, and more accurate than the existing monotone scheme on some kinds of meshes.