中文摘要：

概述对流项离散格式所引起的假扩散现象及选择不同的离散格式对数值计算过程的影响；在分析稳定性可控的对流项离散格式（stability controllable second—order difference scheme，SCSD）的基础上，提出求解二维对流扩散问题时，直接采用块修正技术和PDMA算法的强隐迭代算法，并对该格式在近边界节点的离散方程的处理上采用非均匀网格技术。通过典型算例验证，该方法不仅抑制了假扩散现象，保证了计算精度，同时也使稳定性得到增强。因此，采用SCSD格式离散对流项，应用非均匀网格处理近边界，并将TDMA算法和PDMA算法同时纳入求解离散方程的做法是合理的，整个程序的框架具有很强的通用性。

英文摘要：

The false scaling phenomena resulted from the discretization scheme on the convective term of the incompressible flow equations and the effect of different discretization schemes was first discussed in this paper. In using SCSD （stability controllable second-order difference） scheme for solving 2D convection-diffusion problems, a strong implicit iteration procedure was adopted together with the block correction technology and pentdiagonal matrix algorithm. Non-uniform grid technology was also used for treating the nodes close to the domain boundaries. The scheme was verified via two benchmark problems,namely the lid-driven cavity flow and the natural convection in a cavity. It was shown that the scheme has a rather good calculation stability and accuracy with reduced false scaling. It concluded that the method proposed in this paper is reasonable and the program has a wide applicability.