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为了避免求解高度非线性的三维饱和-非饱和水流方程,本文假设在非饱和带和饱和带中地下水流分别由一维垂向流模型(θ-模型)和二维水平流模型(H-模型)描述。在地下水面的水流通量(qH)是连接θ-模型和H-模型的边界条件。通过将垂向平均含水量-θ(H,t)展开成以H为变量的一阶Taylor级数,qH可表示作为水位(H)的函数。一个双层迭代方案被用于求解饱和-非饱和水流模型,它包括应用有限单元法结合Picard迭代求解非线性的θ-模型、H-模型和应用Taylor级数逐步逼近非线性函数-θ(H,t)的两个迭代过程。算例结果表明:在模型功能方面,该方法实用性强,能够很好地描述饱和、非饱和带水量平衡,较好地反映含水量与地下水位的变化;在计算技术方面,方法思路清晰,求解过程易于程序实现,且两个层次的迭代都具有较快的收敛性。
In order to avoid solving highly nonlinear three-dimensional saturated-unsaturated water flow equations, this paper assumes that the groundwater flow in the unsaturated zone and the saturation zone consists of one-dimensional vertical flow model (θ-model) and two-dimensional horizontal flow model )description. The water flux (qH) at the groundwater level is the boundary condition that connects the θ-model to the H-model. QH can be expressed as a function of water level (H) by unrolling the vertical average moisture content -θ (H, t) into a first-order Taylor series variable with H as a variable. A two-layer iterative scheme is used to solve the saturated-unsaturated water flow model, which includes applying the finite element method combined with the Picard iteration to solving the nonlinear θ-model, the H-model and applying the Taylor series to the nonlinear function -θ (H , t) two iterative process. The results of the example show that the proposed method is practicable in terms of model function and can well describe the water balance of saturated and unsaturated zones, which can well reflect the changes of water content and groundwater level. In terms of computational techniques, The solution process is easy to implement, and the two levels of iteration have faster convergence.