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
主办部门：8455新葡萄场网站数学系
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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