二维对流扩散方程非均匀网格上的高阶紧致差分方法  

A high-order compact difference method for 2D convection-diffusion equation on non-uniform grid

作　　者：田芳[1] 田振夫[2] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021 [2]复旦大学数学科学学院,力学与工程科学系,上海200433

出　　处：《水动力学研究与进展（A辑）》2008年第5期475-483,共9页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金资助项目(10662006)

摘　　要：利用降维法导出了非均匀网格上二维对流扩散方程的高精度紧致差分格式.对于离散得到的代数方程组采用BiCGStab(2)迭代法求解。数值算例表明,在相同网格节点数的情况下,本文基于非均匀网格格式较均匀网格格式具有高精度,高分辨率的优点,对于含边界层的对流扩散问题具有很好的适应性。Based on the method of dimension reduction, a high-order compact finite difference scheme on non-uniform grid is deduced for 2D convection-diffusion equation and a BiCGSTab（2） method （The hybrid bi-conjugate gradient stabilized method） is employed to solve the resulting algebra systems. Two numerical experiments are used to show that the present scheme has many advantages such as yielding more accurate numerical solutions, having high resolution for the boundary layers, being well suitable for both convection-dominant flow and diffusion-dominant flow, and so on. It is also pointed out that the appropriate structure of a non-uniform grid can lead to solution superior to that for a uniform grid structure with the same number of grid points.

关 键 词：对流扩散方程 非均匀网格 高精度紧致差分方法 边界层 

分 类 号：O375[理学—流体力学]