一种改进格林元方法及在渗流问题中的应用

采用格林公式和基本解推导出直接边界积分方程来求解渗流问题.边界积分方程数值离散基于格林元方法(Green element methond),改进了原方法中压力和压力导数的求解方法,命名为混合边界元方法(Mixed boundary element method).相较于格林元类方法,该方法显式考虑了求解节点的外法向流量值和压力值,并使求得的数值解在求解区域上能够连续,符合实际的物理过程,在不增加额外未知数的情况下提高了计算精度.分析了不同网格类型对模拟计算结果的影响,并对稳定渗流问题、非稳定(瞬态)渗流问题和非稳态问题进行了实例计算,结果显示改进方法提高了计算精度,并对各类渗流问题有较好的适应性.

An improved Green element method and its application in seepage problems

In this paper,Green''s formula and basic solutionswere used to derive the direct boundary integral equation to solve the seepage problem.The numerical discretization of the boundary integral equation is based on the Green element method,which improves the solution method of pressure and pressure derivative in the original method.According to the characteristics of the method,the method is named as the mixed boundary element method.Compared with the Green element method,this method explicitly considers the external normal flow value and pressure value of the solution node,and enables the obtained numerical solution to be continuous in the solution area,conforming to the actual physical process,and improved calculation accuracy without increasing the number of unknowns.The influence of different grid types on the simulation calculation results is analysed,and the steady seepage problem, the unsteady (transient) seepage problem and the unsteady state problem are calculated. The results show that the improved method improves the calculation accuracy,and the seepage problem has better adaptability.