饱和-非饱和带地下水流数值模型的双层迭代方法  

Double iteration scheme for numerical model of groundwater flow in saturated-unsaturated zone

作　　者：刘春平[1,2] 高萍[1] 

机构地区：[1]防灾科技学院,河北三河燕郊065201 [2]湖南师范大学资源与环境科学学院,长沙410006

出　　处：《工程勘察》2009年第8期33-37,共5页Geotechnical Investigation & Surveying

基　　金：科技部地震行业科研专项项目(200808055);湖南省教育厅重点项目(06A039)

摘　　要：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。The computational burden and instability of the fully 3-D saturated-unsaturated unified approach could be lessened considerably by using the assumption of the 1-D vertical flow model （θ-model） in unsaturated zone and 2-D horizontal flow model （H-model） in saturated zone. The water flux （ qH ） on groundwater table is the boundary conditions for both of θ-model and H-model, and numerically it is expressed into the equation just including groundwater table （H） by applying one-order Taylor series to unfold average water-content θ （ H, t） . A double iteration schemes is developed for solving the saturated-unsaturated flow model. The finite element method combined with Picard iteration is used to solve the nonlinear θ-model and H-model in first-layer iteration. The water fluxes （q.） are gradually improved in second-layer iteration by substituting the new water tables （H） generated by first-layer iteration into the equation θ （ H, t） expressed by one-order Taylor series. A hypothesis example is used to test the model accuracy and numerical simulation technique. It shows that there are good descriptions for water equilibriums and the changes of the water content and water table in the saturatedunsaturated zone.

关 键 词：饱和-非饱和带 数值模拟 地下水 

分 类 号：P641.2[天文地球—地质矿产勘探]