二维对流扩散方程基于三角形网格的特征差分格式  

CHARACTERISTIC DIFFERENCE SCHEMES ON TRIANGULAR MESH FOR 2D CONVECTION DIFFUSION EQUATIONS

作　　者：王同科[1] 

机构地区：[1]天津师范大学数学科学学院

出　　处：《数值计算与计算机应用》2003年第3期177-188,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(项目编号:19972039)

摘　　要：§1.引言 对流扩散方程描述了众多的物理现象,其数值算法研究一直受到重视[1～6,13～14].在这方面,特征差分方法和特征有限元方法是非常有效的两种方法[1～6].特征差分方法计算简单,但适应区域不够灵活.This paper presents two characteristic difference schemes on triangular mesh for two-dimensional linear and nonlinear convection-diffusion equations. It is proved that the two methods satisfy discrete maximum principle and they are stable in discrete maximum norm. It is also proved that they converge in discrete maximum norm and the first one has first order accuracy for convection term and the other has second order accuracy for convection term, which is especially suitable for solving strong convection-dominated diffusion problems. Finally, numerical examples show that these methods are very effective for solving convection-dominated diffusion problems.

关 键 词：二维对流扩散方程 三角形网格 特征差分格式 偏微分方程 收敛性 非线性方程 向后Euler型 

分 类 号：O241.84[理学—计算数学]