非均匀网格上求解对流扩散问题的高阶紧致差分方法

基于非均网格上函数的泰勒级数展开,推导出求解一维对流扩散问题的高阶紧致差分格式.对于离散化得到的代数方程组,采用BiCGStab（2）迭代法求解.数值实验表明,该格式对于扩散占优、对流占优及边界层问题都有很好的适应性,对于数值模拟待求物理量的大梯度变化具有很高的分辨率,计算结果明显优于传统的均匀网格上的差分格式.在具体的数值模拟中,可根据实际物理量的变化规律,选取适当的网格生成变换函数,合理地调整非均匀网格的疏密分布,从而获得比在含相同结点数的均匀网络系统中更为精确的数值结果.

A High-Order Compact Finite Difference Method for Convection Diffusion Problems on Non-uniform Grids

Based on Taylor＇s series expansion of continuous function, a high order compact finite difference scheme on non-uniform grid for 1D steady convection diffusion problems is developed. BiCGStab （2） method is employed to solve the resulting algebraic systems of equations. Compared with some conventional difference schemes, the present scheme has many advantages such as yielding more accurate numerical solutions, having high resolution for the large gradient changes of the unknown quantity, being well suitable for both convection-dominant flow and diffusion-dominant flow, and so on. It is also point out that the appropriate structure of a non-uniform grid can lead to a solution superior to that for a uniform grid structure with the same grid points.