一种基于变分的网格运动方法及其在边界层问题数值求解中的应用  

A Moving Mesh Method Based on Variational Problem for Boundary Layer Problem

作　　者：李征[1] 王双虎[1] 

机构地区：[1]北京应用物理与计算数学研究所,北京100088

出　　处：《南京师大学报（自然科学版）》2007年第2期15-21,共7页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家973重点基础研究发展计划(2005CB32170X)资助项目

摘　　要：从控制网格以适应解的性态并具有一定光滑性的朴素思想出发,建立了一种基于变分的网格运动方法,并给出了两种简单的数值求解方法.以两点边值问题及边界层问题为例,对这一网格运动方法进行了数值试验并得到了满意的数值结果,结果说明本方法成功地控制了网格的分布.A new moving mesh method is given in this dissertation. Key idea of our method is that the mesh should adapt the solutions＇ character and have some smoothness. The distribution of the nodes is gotten by a variational problem, whose Euler-Lagrange equation is the new moving mesh equation. Why and how to form the new method is introduced in details. Numerical results in two-point boundary problems and boundary layer problems are very encouraging and clearly to show that in many cases the method can control the mesh motion.

关 键 词：运动网格 变分法 控制函数 欧拉-拉格朗吕方程 

分 类 号：O242.21[理学—计算数学]