非匹配网格上求解扩散方程的高精度结点值重构算法  

THE CONSTRUCTION OF CELL-CENTERED DIFFUSION SCHEMES ON NON-CONFORMING MESHES USING A NEW RECONSTRUCTION ALGORITHM

作　　者：常利娜[1] 袁光伟[1] 曾清红[1] 

机构地区：[1]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》2016年第1期57-66,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11571048;11371068;11271054);中物院科学技术发展基金(2014A0202010;2015B0202040);计算物理重点实验室基金(9140C690202150C69304)资助

摘　　要：构造了非匹配网格上求解多介质扩散问题的高精度格式.格式中只包含单元中心未知量,物理意义明确,易于实施,适用于模拟复杂的实际工程问题.格式的特点在于,给出了由中心未知量重构结点未知量的显式表达式,对非匹配网格上的内点和悬点,这一表达式具有统一的形式.在非匹配随机网格上进行数值实验,结果显示,格式对强间断问题和非线性问题都具有二阶精度.A new diffusion scheme is constructed for solving multi-material problems on nonconforming meshes. There are only cell-centered unknowns in this scheme. And the scheme is simple and easy to be applied. So it is suitable for the numerical simulation of complicated problems in engineering. The main characteristics of the scheme is that an explicit expression is given so that the vertex values can be reconstructed with the cell-centered ones. Moreover, the values at the inner vertex are approximated using the same method as that for the ones at the hanging vertex. Numerical results show that the scheme is second order accurate for the discontinuous and nonlinear problems on random non-conforming meshes.

关 键 词：扩散方程 多介质 单元中心型格式 非匹配网格 

分 类 号：O241.8[理学—计算数学]