Seminar第1530期 各项异性扩散问题的保正定性中心节点格式

创建时间:  2017/11/15  谭福平   浏览次数:   返回

报告主题:各项异性扩散问题的保正定性中心节点格式
报告人:邬吉明 研究员 (北京应用物理与计算数学研究所)
报告时间:2017年 11月21日(周二)10:00
报告地点:校本部G507
邀请人:刘东杰 

报告摘要:We suggest a new positivity-preserving finite volume scheme for anisotropic diffusion problems on arbitrary polygonal grids. The scheme has vertex-centered, edge-midpoint and cell-centered unknowns. The vertex-centered unknowns are primary and have finite volume equations associated with them. The edge-midpoint and cell-centered unknowns are treated as auxiliary ones and are interpolated by the primary unknowns, which makes the final scheme a pure vertex-centered one. Unlike most existing positivity-preserving schemes, the construction of the scheme is based on a special nonlinear two-point flux approximation that has a fixed stencil and does not require the convex decomposition of the co-normal. Numerical experiments demonstrate the second-order accuracy and well positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids. Moreover, the proposed scheme does not have the so-called numerical heat barrier issue suffered by most existing cell-centered and hybrid schemes.


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