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摘要:
在使用网格单元中心差分格式的地下水模型中，对地下水网格单元“疏干（干）-湿润（湿）转化”的模拟极易引发模型迭代不收敛等异常情况，很大程度上影响模型的应用。本研究使用理想案例和丹麦应用实例，综合比较了MODFLOW模型的试算法与COMUS模型的全有效单元法对网格单元“干-湿转化”问题的模拟能力及算法特性。结果表明：（1）试算法的参数组合选取对模拟的收敛性和模拟结果都有明显影响，使用试算法时需要不断优化参数组合以避免模型迭代不收敛或模拟失真等异常情况，很大程度上增加了用户使用模型的难度和时间成本；（2）全有效单元法的模拟结果比试算法的模拟结果更具可靠性，全有效单元法的作用等同于理论上最优的试算法参数组合，使用全有效单元法时用户无需进行复杂的参数组合工作，因此该方法能有效降低模型的使用难度与模拟结果的不确定性；（3）全有效单元法中单元间水平向水力传导度算法实现了可以与经典调和平均法相比较的数值计算精度，说明全有效单元法在不涉及网格单元“干-湿转化”问题的地下水模拟中同样具有应用潜力。综上所述，全有效单元法更适用于处理地下水模型单元的疏干-湿润转化问题，并且有望在地下水数值模拟领域中得到更为广泛的应用。
Abstract:When simulating drying-rewetting process of grid cells in numerical groundwater modeling using the block-centered finite-difference approach, the models is highly probable to run into non-convergence, which could greatly affect the applicability of groundwater models. This study used ideal case and practical simulation in Denmark to comprehensively compare the simulation capabilities and characteristics of two algorithms, namely the empirical trial (ET) method proposed by MODFLOW and the always active cell (AAC) method proposed by COMUS, in the drying-rewetting simulation. The results show that: (1) For the ET method, the selection of parameter combination has a significant influence on the model convergence and the simulation results. It is compulsory to continuously optimize the parameter to avoid model failures such as non-convergence and large simulation errors when using the ET method, which greatly increases the difficulty of groundwater model application and time cost. (2) The simulation results from the AAC method are more reliable than those from the ET method. Theoretically, the effect of the AAC method is equivalent to the optimal parameter set in the ET method. Therefore, parameter optimization is no longer needed in the AAC method, which can effectively reduce the difficulty of using groundwater models and meanwhile reduce the uncertainty of simulation results. (3) The numerical accuracy of the intercell horizontal hydraulic conductance in the AAC method is consistent with that of the classical harmonic average method, demonstrating that the AAC method can also be used in the simulation without the drying-rewetting process. In summary, the AAC method is more suitable for simulating the drying-rewetting process of groundwater model cells and is expected to be more widely used in groundwater numerical simulation.
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表 1 理想案例水量平衡模拟结果对比
Table 1. Comparison of water balance in the ideal case
/m3 水量平衡通量 VS2DT 试算法方案 全有效单元法方案 定水头边界流入量 364.659 416.470 362.310 井流开采量 −400.000 −400.000 −400.000 蓄变量 −35.341 16.470 −37.690 水量平衡误差 0.000 0.000 0.000 
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表 2 Hampen湖流域模型模拟方案设置与模拟收敛性
Table 2. Simulation scheme settings and convergence of the Lake Hampen basin model
模拟方案参数 试算法1 试算法2 试算法3 试算法4 试算法5 试算法6 试算法7 全有效
单元法WETDRY/m 0.3 0.3 0.3 0.3 1 2 −0.02 NWETIT 2 2 2 4 2 2 2 WETFCT 0.1 1 1 1 1 1 1 IHDWET 1 1 2 2 2 2 2 模拟结果 不收敛 不收敛 不收敛 收敛 收敛 收敛 收敛 收敛
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表 3 试算法方案与全有效单元法方案模拟的水量平衡对比
Table 3. Comparison of simulated water balance by the ET schemes and the AAC scheme
/104 m3 水量平衡通量 试算法4 试算法5 试算法6 试算法7 全有效单元法 面上补给量 7874.093 7874.078 7874.101 7874.084 7874.061 通用水头边界流入量 1063.619 1064.806 1061.605 1069.624 1070.379 河道渗漏补给量 16.038 16.315 17.247 16.134 16.473 湖泊渗漏补给量 1528.940 1526.667 1509.230 1532.026 1526.061 通用水头边界流出量 8822.492 8823.179 8823.343 8826.603 8811.780 地下水向河道的排泄量 16.377 16.459 18.065 15.915 16.212 地下水向湖泊的排泄量 1601.177 1604.219 1638.722 1595.755 1596.793 潜水蒸发量 0.000 0.000 0.000 0.000 0.000 蓄变量 42.641 38.008 −17.949 53.597 62.189 水量平衡误差 0.002 0.001 0.003 −0.002 0.000
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