二维线性对流扩散方程一种新的特征差分算法及收敛分析  

A New Kind of Characteristic-Difference Algorithm for Linear Convection-Diffusion Equation of Two Dimensions and Convergence Analysis

作　　者：张宏伟[1] 胡能兵[1] 周宽宽[1] 

机构地区：[1]长沙理工大学数学与计算科学学院,长沙410076

出　　处：《四川理工学院学报（自然科学版）》2008年第6期1-5,共5页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(10771021);省教育厅优秀青年项目(06B003)

摘　　要：文章讨论了二维线性对流扩散方程,将特征线法和有限差分法相结合,借助于双线性插值,给出了求解二维线性对流扩散方程数值解的一种新的特征差分格式,并分析了该算法的收敛性。此算法表明对于一类对流扩散方程,应用此差分格式,能更有效地消除数值振荡现象,从而极大地提高数值逼近度。Linear convection-diffusion equation of two-dimensions is discussed. A new kind of characteristicdifference algorithm is for linear convection-diffusion equation of two-dimensions, constructed by combining characteristic method with the finite-difference method and with the help of bilinear interpolation method.And it analyses the convergence of this characteristic-difference algorithm.This algorithm shows that it can eliminate the numerical oscillations more efficiently by the application of this difference format for a category of convection-diffusion equations and can greatly improve the approximation rate of numerical value.

关 键 词：二维对流扩散方程 特征差分法 收敛分析 

分 类 号：O241.82[理学—计算数学]