对流扩散问题的交替方向差分-流线扩散格式

ALTERNATING-DIRECTION DIFFERENCE-STREAMLINE DIFFUSION METHOD FOR CONVECTION-DIFFUSION EQUATION

1.引 言 差分-流线扩散法（Finite Difference-Streamline Diffusion Method,简称FDSD方法）于1998年由文[1]提出并对线性对流占优扩散问题给出分析,随后文[2],[3]就非线性问题的FDSD格式及FDSD预测-校正格式,分别作出了分析,文[4]讨论了FDSD方法的后验估计及自适应技术,[5],[6]则分别讨论了FDSD方法的某些重要应用.与基于时-空有限元的传统流线扩散法相比,FDSD方法的计算工作量已有成数量级的减少,且较易于推广到非线性问题,然而,对于高维问题,在每一时间层,仍然需要求解一大型线性或非线性方程组,工作量仍然很大.参照J.Douglas与T.

In this paper, based on the combining of Alternating-Direction procedure with Finite Difference-Streamline Diffusion (FDSD) method, an alternate direction difference streamline diffusion scheme is proposed for two dimension linear convection diffusion equation. The analysis of stability and the estimation error for the considered scheme are given.