Wang Quanrong, Zhan Hongbin, Tang Zhonghua
School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, China.
Ground Water. 2014 Nov-Dec;52(6):924-35. doi: 10.1111/gwat.12142. Epub 2013 Dec 2.
The nonhorizontal-model-layer (NHML) grid system is more accurate than the horizontal-model-layer grid system to describe groundwater flow in an unconfined sloping aquifer on the basis of MODFLOW-2000. However, the finite-difference scheme of NHML was based on the Dupuit-Forchheimer assumption that the streamlines were horizontal, which was acceptable for slope less than 0.10. In this study, we presented a new finite-difference scheme of NHML based on the Boussinesq assumption and developed a new package SLOPE which was incorporated into MODFLOW-2000 to become the MODFLOW-SP model. The accuracy of MODFLOW-SP was tested against solution of Mac Cormack (1969). The differences between the solutions of MODFLOW-2000 and MODFLOW-SP were nearly negligible when the slope was less than 0.27, and they were noticeable during the transient flow stage and vanished in steady state when the slope increased above 0.27. We established a model considering the vertical flow using COMSOL Multiphysics to test the robustness of constrains used in MODFLOW-SP. The results showed that streamlines quickly became parallel with the aquifer base except in the narrow regions near the boundaries when the initial flow was not parallel to the aquifer base. MODFLOW-SP can be used to predict the hydraulic head of an unconfined aquifer along the profile perpendicular to the aquifer base when the slope was smaller than 0.50. The errors associated with constrains used in MODFLOW-SP were small but noticeable when the slope increased to 0.75, and became significant for the slope of 1.0.
基于MODFLOW - 2000，非水平模型层（NHML）网格系统在描述无压倾斜含水层中的地下水流方面比水平模型层网格系统更为精确。然而，NHML的有限差分格式基于达西 - 福希海默假设，即流线是水平的，对于坡度小于0.10的情况是可以接受的。在本研究中，我们提出了一种基于布辛涅斯克假设的NHML新有限差分格式，并开发了一个新的程序包SLOPE，将其并入MODFLOW - 2000中形成MODFLOW - SP模型。针对Mac Cormack（1969）的解对MODFLOW - SP的精度进行了测试。当坡度小于0.27时，MODFLOW - 2000和MODFLOW - SP的解之间的差异几乎可以忽略不计，而在瞬态流阶段差异明显，当坡度超过0.27时在稳态下差异消失。我们使用COMSOL Multiphysics建立了一个考虑垂直流的模型，以测试MODFLOW - SP中使用的约束的稳健性。结果表明，当初始流不平行于含水层底面时，除了边界附近的狭窄区域外，流线很快与含水层底面平行。当坡度小于0.50时，MODFLOW - SP可用于预测无压含水层沿垂直于含水层底面的剖面的水头。当坡度增加到0.75时，与MODFLOW - SP中使用的约束相关的误差较小但明显，而对于坡度为1.0时误差变得显著。
