非规则区域中拉普拉斯方程的有限分析5点格式

建立了非规则区域的有限分析5点格式，增加了有限分析法对不规则边界的适应性。应用所提出的方法对水利工程中常见的有压和无压流动进行了计算，与实验和前人的计算结果相比较，本文的方法都能得到较为满意的结果。本文的计算格式也可以应用到其他非规则区域的计算中。

The 5-point finite analytic schemes for laplace equation in irregular domains

Finite Analytic Method is one of the effective schemes for solving convection diffusion equation. In former studies, the irregular five-point boundary element is recasted into the nine-point element, allowing a regular structural grid system to be used to solve for the water flow in an irregular domain. This scheme can only be used to calculate the convection-diffusion equation. The new scheme of finite analytic method for Laplace equation in irregular domain is got by coordinate rotation technique in this paper. This method entails the nine-point element and five-point element such that it can simulate quite well the irregular flow domain without using boundary-fitted transformation. The seepage flow and the flow under sluice gate are simulated by this method. The calculated result fitted well with the experiment data in seepage flow. In the flow under sluice gate, the surface profiles of upstream and downstream are compared with results of the analytical solution and boundary-fitted transformation solution.