扩散方程九点格式中节点未知量的一种新的插值算法  

A NEW NODAL INTERPOLATION ALGORITHM IN NINE POINT SCHEME FOR DIFFUSION PROBLEMS

作　　者：董成 邬吉明[2] DONG Cheng;WU Ji-ming(Graduate School of China Academy of Engineering Physics,Beijing 100088,China;Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)

机构地区：[1]中国工程物理研究院研究生院,北京100088 [2]北京应用物理与计算数学研究所,北京100088

出　　处：《数学杂志》2019年第2期203-215,共13页Journal of Mathematics

基　　金：国家自然科学基金资助(11271053;11671313)

摘　　要：本文研究了二维扩散方程九点格式中节点辅助未知量的插值问题.利用多点通量逼近的边未知量插值算法和一个特殊的极限技巧,获得了节点辅助未知量的一个新的插值算法,并在给定假设下严格分析了该算法中局部线性系统的可解性.新算法满足线性精确准则,具有较高的精度.In this paper,we discuss the interpolation problem for nodal auxiliary unknowns in nine point scheme for 2D diffusion problems.By applying a special limit technique to the edge interpolation algorithm in multipoint flux approximation,we obtain a new nodal interpolation algorithm.Moreover,the solvability of the local system in the interpolation algorithm is analyzed rigorously under certain assumptions.The new algorithm satisfies linearity preserving criterion and has a second-order accuracy.

关 键 词：扩散方程 九点格式 节点未知量插值 线性精确 

分 类 号：O241.82[理学—计算数学]