Fitts Charles R
Geosciences Department, University of Southern Maine, ME 047038, USA.
Ground Water. 2006 Jan-Feb;44(1):99-101. doi: 10.1111/j.1745-6584.2005.00082.x.
Although most current applications of the analytic element method are formulated for isotropic hydraulic conductivity, anisotropic domains can be modeled with analytic elements using the well-known coordinate transformation where one coordinate axis is scaled by the square root of the anisotropy ratio. If the standard analytic solution for steady radial flow to a well is used with this coordinate transformation, the resulting solution correctly models the far field but it does not meet the constant head boundary condition at the well radius. This could be a significant shortcoming if you are interested in the flow field close to the well or want to estimate the head at the pumping well. A new solution for two-dimensional steady flow to a well in an anisotropic domain is presented. This solution satisfies the governing equations exactly and meets the constant head boundary condition at the well radius exactly. It was derived using a conformal mapping.
尽管目前解析单元法的大多数应用都是针对各向同性水力传导率制定的，但对于各向异性区域，可以使用解析单元通过著名的坐标变换进行建模，其中一个坐标轴按各向异性比率的平方根进行缩放。如果将稳定径向流到井的标准解析解与这种坐标变换一起使用，得到的解能正确模拟远场，但在井半径处不满足恒定水头边界条件。如果您对靠近井的流场感兴趣或想估计抽水井处的水头，这可能是一个重大缺点。本文提出了一种各向异性区域中二维稳定流到井的新解。该解精确满足控制方程，并在井半径处精确满足恒定水头边界条件。它是通过保角映射推导出来的。
