各向异性扩散方程的高精度算法  

HIGH ACCURATE COMPUTATION OF DIFFUSION EQUATIONS WITH ANISOTROPIC COEFFICIENTS

作　　者：宋淑红[1] 王双虎[1,2] 

机构地区：[1]北京应用物理与计算数学研究所,北京100094 [2]北京应用物理与计算数学研究所计算物理实验室,北京100088

出　　处：《数值计算与计算机应用》2017年第4期312-326,共15页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金项目(11001024;11501040;u1630247)资助

摘　　要：针对多介质各向异性扩散方程,本文设计了一种非结构多边形网格高精度有限体积计算格式.为了能适应网格大变形,在构造格式框架时除了用到单元中心量外还引入了节点量作为中间变量,并通过推广孪生逼近算法于各向异性扩散系数情形消除节点量,使算法回归于单元中心量计算流程.数值算例表明,该方法能较好适应大变形网格及间断系数各向异性扩散方程计算.In this paper, a high accurate finite volume method is given for diffusion equations with anisotropic diffusion coefficients on unstructured meshes. In order to deal with distorted meshes, the vertex unknowns are introduced as the middle quantities in the construction of this method besides the cell-centered unknowns. The ＂twin-fitting＂ method is applied to computing the vertex unknowns for diffusion equations with anisotropic coefficients, so that the resulting method is solved by the cell-centered unknowns. Numerical experiments show that this method can deal with distorted meshes and anisotropic diffusion coefficient problem.

关 键 词：各向异性扩散系数 孪生逼近 节点量计算方法 大变形网格 

分 类 号：O241.8[理学—计算数学]