非均匀网格上三维对流扩散方程高精度紧致差分方法

A High Accuracy Compact Difference Method for 3D Convection-diffusion Equation on Non-uniform Grid

利用降维法推导出非均匀网格上三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,在网格节点数相同的情况下,基于非均匀网格的计算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有很好的适应性.

Based on the method of dimension reduction, a high accuracy compact finite difference scheme on non-uniform grid is deduced for 3D convection-diffusion equation and the BiCGStab（2） method （the hybrid bi-conjugate gradient stabilized method） is employed to solve the resulting algebra systems. A numerical experiment is 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 and diffusion-dominant problems, and so on. It is also pointed 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 number of grid points.