Overview of the Finite Element Method in Groundwater Hydrology
Overview of the Finite Element Method in Groundwater Hydrology
复制标题
地下水水文学有限元方法概述
DOI：
10.1007/978-3-662-02348-8_2
复制
发表时间：
1982
影响因子：
1.4
通讯作者：
P. Witherspoon
中科院分区：
文献类型：
--
作者：
T. Narasimhan;P. Witherspoon
自 20 世纪 60 年代中期引入地下水文献以来，有限元方法已发展成为分析各种地下水流问题的非常强大的数值工具。该方法的应用涵盖多含水层系统中的流动、自由表面流动、饱和-非饱和流动、地面沉降、裂隙-多孔系统以及稳定或非稳定条件下的大型地下水盆地。该方法的强大之处在于它使用一种非常通用的技术来评估流域内任何点上任何方向的空间梯度。该方法通过感兴趣点处守恒方程的积分表述补充了这一优点。即使感兴趣的问题具有复杂的几何形状，这种方法产生的算法也允许相对简单的几何输入。从概念角度来看，有理由怀疑有限元方法的替代公式是可能的，其中放弃加权积分技术以支持积分子域的明确定义。除了节点坐标和元素列表之外，还可以通过输入预处理几何输入的选项来增强现有有限元算法的灵活性。从守恒积分直接公式化有限元方程可能提供一种值得关注的替代方案。随着微型计算机的出现，有限元方法有望成为 20 世纪 80 年代执业工程师的日常工具。
Since its introduction into the groundwater literature during the mid 1960’s, the finite element method has developed into a very powerful numerical tool for analyzing a variety of groundwater flow problems. Applications of the method cover flow in multi-aquifer systems, flow with a free surface, saturated-unsaturated flow, land subsidence, fractured-porous systems, and large groundwater basins under steady or nonsteady conditions. The method derives its power from the fact that it uses a very general technique for the evaluation of spatial gradients in any direction at any point within the flow domain. This advantage is complemented in the method by an integral statement of the conservation equation at the point of interest. The algorithms stemming from this approach permit relatively simple geometric inputs, even when the problem of interest has complex geometries. From a conceptual perspective there is reason to suspect that alternate formulations of the finite element method may be possible in which the weighted integration technique is dispensed with in favor of an explicit definition of the subdomains of integration. The flexibility of existing finite element algorithms may be enhanced by having options for inputting preprocessed geometric inputs in addition to nodal point coordinates and element lists. Direct formulation of the finite element equations from conservation integrals may provide an alternative that deserves attention. With the advent of mini computers, the finite element method promises to become an every day tool for the practising engineer during the 1980’s.