地下水非稳定流问题的有限分析五点格式

FIVE-POINT ELEMENT SCHEME OF FINITE ANALYTIC METHOD FOR UNSTEADY GROUNDWATER FLOW

针对有限分析法不规则单元适应性差的问题,采用坐标旋转技术,建立了一种求解地下水非稳定流方程的有限分析五点格式,并给出了相应的边界条件。应用所提出的地下水非稳定流方程的有限分析五点格式对地下水的3个典型问题进行了模拟计算,其结果与解析解和前人的计算结果相比较,计算得到的结果与解析解吻合很好,较有限元法、边界元法的精度高,计算过程简单,稳定性好,收敛速度快,能很好地拟合边界和非均质分区界线,确切反映渗流场中不同部位的水头分布,并能较好地适应于复杂的几何区域。计算格式也可以应用到其他非规则区域的计算中。

In view of the adaptability of finite analytic method for irregular unit,a five-point element scheme of finite analytic method was established in the present study to solve unsteady groundwater flow equation. The three typical questions of groundwater were calculated with the method proposed. In comparison with the analytic solution and predecessor＇s computed result,the result of the 5-point element scheme of finite analytic method tallies well with analytic solution and has higher precision than the solution of finite element and boundary element. Moreover, it is shown that it has a simple computational process, good stability and quick convergence rate,and it can adapt well in complex geometry region. It is proposed that the computational form reported in this paper may also be applied in other irregular region.