求解三维非定常对流扩散方程的隐式差分方法  

Implicit difference method for the 3-D unsteady convection diffusion equation

作　　者：黄文艳[1] 刘富祥[1] 葛永斌[1] 

机构地区：[1]宁夏大学应用数学和力学研究所,宁夏银川750021

出　　处：《东北师大学报（自然科学版）》2009年第4期42-47,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10502026;10662006);宁夏自然科学基金资助项目(NZ0937)

摘　　要：提出了一种数值求解三维非定常变系数对流扩散方程,对角占优、空间为二阶精度的隐格式,利用Fourier分析方法证明了该格式是无条件稳定的,并且由于格式具有对角占优性,因此适合于大梯度(高雷诺数)问题的数值求解.另外,为了克服传统迭代法在求解隐格式时收敛速度慢的缺陷,采用了多重网格加速技术,大大加快了迭代收敛速度,提高了求解效率.数值实验结果证明了该方法的精确性、稳定性和对高网格雷诺数问题的强适应性.A diagonally dominant second-order accurate implicit scheme is proposed to solve the threedimensional unsteady conveclion diffusion equation with variable coefficients. It is proved uncondition ally stable by fourier analysis. Because the scheme is diagonally dominant, it suits the solution of large gradient problems（high Reynolds number problems）. On the other hand,a muhigrid method 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 experiments are employed to show that the present method is stable and yields accurate solution for high Reynolds number problems.

关 键 词：对流扩散方程 二阶精度隐格式 对角占优 无条件稳定 多重网格方法 

分 类 号：O241.82[理学—计算数学]