常系数对流扩散方程的一种数值解法  

A Numerical Solution of the Convective Diffusion Equation with Constant Coefficient

作　　者：阿米娜·沙比尔 杨庆之[1,2] Amina·Shabier;Yang Qingzhi(School of Mathematical Sciences and LPMC,Nankai Univrsity,Tianjin 300071,China;School of Mathematics and Statistics,Kashgar University,Kashgar 844006,China)

机构地区：[1]南开大学数学科学学院,天津300071 [2]喀什大学数学科学学院,新疆喀什844006

出　　处：《南开大学学报（自然科学版）》2020年第5期33-44,共12页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2017D01A14)。

摘　　要：讨论了一维常系数对流扩散方程的一种数值解法.对于对流占优和扩散占优的情况,分别构造了相应的隐式差分格式,分析了截断误差、收敛和稳定性.理论分析和数值实验结果表明,该隐式差分格式有效地消除了对流主导所引起的数值振荡,控制了扩散主导引起的耗散问题,并且可以在保持差分格式的所有优点的基础上直接推广到二维问题.最后在此基础上给出了一种隐式分裂中心差分算法.A numerical method of constant coefficient convection diffusion equation is studied.An im-plicit difference scheme is established for convective dominance and diffusion dominance respectively.The truncation error,convergence and stability of this scheme are discussed.Theoretical analysis and experimen-tal results show that when the grid ratio is properly selected,the difference scheme is quite stable.It can be extended directly to the two--dimensional problem,and all the advantages of the difference scheme can be maintained.On this basis,an implicit split center difference algorithm is presented.

关 键 词：对流占优 扩散占优 二维对流-扩散方程 隐式差分格式 

分 类 号：O241.8[理学—计算数学]