中文摘要：

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。

英文摘要：

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.