承压含水层地下水稳定流的有限层分析

Analysis of steady under-groundwater flow in the confined aquifer by finite layer method

有限层法是一种对空间某一方向进行数值离散,而在其余两方向采用连续函数的半数值半解析方法.该方法能有效地将三维问题简化为一维问题求解,从根本上解决了常用数值分析方法在模拟三维地下水运动时存在的计算工作量大、占用内存多、耗时大等缺点.文中基于有限层法的优点,推导了以伽辽金法结合贝塞耳函数为基础的层状非均质各向异性承压含水层的稳定流有限层方程,并编制了相应的计算程序.通过对2个经典算例的数值解与解析解对比分析,验证了该方法的正确性.

The finite layer method （FLM） is a quasi-numerical and quasi-analytic method, which is to discretize one dimension of the spatial domain using finite elements, approximating variations in the other two dimensions by continuous function. The method therefore simplifies three-dimensional problems to one-dimensional ones effectively. The FLM can resolve the disadvantages of common numerical methods to simulate three-dimensional groundwater flows radically, such as the large amount of calculation, the need of much internal storage for computer more calculation time and so on, with common numerical methods to simulate three-dimensional under-groundwater flows. Taking advantages of the FLM, finite layer formulas were derived for calculating the under-groundwater drawdown in the heterogeneous and anisotropic confined aquifer based on Galerkin method and Bessel function, and a computer program on FORTRAN language was developed. Two numerical examples were presented and compared with analytical solutions to demonstrate the validity of finite layer method.