二维非定常对流扩散方程的隐式多重网格方法  

Multigrid Method Based on Implicit Scheme of the 2-D Unsteady Convection Diffusion Equation

作　　者：田瑞雪[1] 葛永斌[2] 吴文权[1] 

机构地区：[1]上海理工大学城市建设与环境工程学院,上海200093 [2]上海理工大学动力工程学院,上海200093

出　　处：《西南师范大学学报（自然科学版）》2003年第4期507-512,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(59876023);上海理工大学创新基金资助项目.

摘　　要：提出了数值求解二维非定常对流扩散方程的一种新的加权平均隐格式,利用Fourier分析方法证明了该格式是无条件稳定的.利用多重网格加速技术,提出了基于时间修正的多重网格的全近似格式(FAS),从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷,大大加快了迭代收敛速度,提高了问题的求解效率.数值计算结果表明,修正的多重网格FAS格式较传统的多重网格粗网格校正格式(CS)具有更好的收敛效率.并且随着σ和s的增大,它可以将传统迭代法的收敛速度提高几十倍,甚至几百倍.A weighted average implicit difference scheme for the twodimensional unsteady convection diffusion equation is proposed and proved unconditional stable by Fourier analysis. A revised multigrid full approximation scheme(FAS) is presented to overcome the difficulties when traditional relaxation methods are used to treat the implicit difference schemes and a fast solution is obtained. Numerical results show that the method is more efficient than the traditional multigrid correction scheme(CS) and its efficiency can be scores or hundreds of that of the traditional relaxation method with increment of σ and s. 

关 键 词：二维非定常对流扩散方程 隐式多重网格方法 加权平均隐格式 FOURIER分析 多重网格全近似格式 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]