求解一维非定常对流扩散方程的紧致差分格式  

The Compact Difference Scheme for Solving 1D Unsteady Convection-Diffusion Equations

作　　者：王小妹 陈豫眉 张嘉杰[1] WANG Xiaomei;CHEN Yumei;ZHANG Jiajie(School of Mathematics and Information, China West Normal University, Nanchong Sichuan 637009;School of Mathematics Education, China West Normal University, Nanchong Sichuan 637009;Institute of Computing Method and Application Software, China West Normal University, Nanchong Sichuan 637009)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009 [3]西华师范大学计算方法及应用软件研究所,四川南充637009

出　　处：《绵阳师范学院学报》2022年第5期7-11,31,共6页Journal of Mianyang Teachers＇ College

基　　金：国家自然科学基金面上项目(11971094);四川省科技厅项目(2017JY0186);西华师范大学英才基金项目(17YC371).

摘　　要：本文基于指数变换与逆变换推导出了一维非定常对流扩散方程的紧致差分格式.首先引入变换将非定常对流扩散方程转化为含源项扩散方程,其次利用紧致差分法求解,该时间方向具有二阶精度,空间方向具有四阶精度.最后通过分析方法给出格式的稳定性分析,并用数值算例验证了格式的精确性和可靠性.A compact difference scheme for one-dimensional unsteady convection-diffusion equations is derived based on exponential transformation and inverse transformation.Firstly,the unsteady convection-diffusion equation is transformed into a diffusion equation with source term by introducing transformation,and then the compact difference method is used to solve the equation.The time direction has second order accuracy,and the space direction has fourth order accuracy.Finally,the stability analysis of the scheme is given by the von Neumann method,and the accuracy and reliability of the scheme are verified by numerical examples.

关 键 词：非定常 对流扩散 差分 紧致格式 稳定性 

分 类 号：O241.82[理学—计算数学]