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众所周知,正确的数学模型是资源评价工作正确进行的必要前提,而有关的计算方法则是探讨模型的手段。随着人们对复杂的渗流机理研究和水文地质条件认识的深化及现代数学技术的发展,有关越流理论的探讨逐步获得进展。继M.S.汉土什和O.E.雅各布之后,S.P.纽曼与威瑟斯庞进一步就相邻含水层水头随抽水层开采发生变化且同时考虑弱透水层弹性储量的越流系统给出了数学模型及理论解。在模型中假设含水层为均质且各向同性、平面无限边界以及允许有一个开采含水层的情况。然而广泛存在非均质各向异性、不规则的有限边界和不同类型边界条件以及两个(或更多)开采层的复杂越流系统。
As we all know, the correct mathematical model is the necessary prerequisite for resource assessment work correctly, and the relevant calculation method is to explore the model. With the deepening understanding of the complicated seepage mechanism and understanding of hydrogeological conditions and the development of modern mathematical techniques, the discussion on the theory of over-flow has made progress gradually. Following MS Han Tosh and OE Jacob, SP Newman and Witherspoon further developed a mathematical model of the over-flow system in which adjacent aquifer heads change with the pumping of the aquifer, taking into account the elastic reserves of the aquitard Theoretical solution. It is assumed in the model that the aquifer is homogeneous and isotropic, with an infinite plane boundary, and that a permissible aquifer is mined. However, there are widespread heterogeneous anisotropy, irregular finite boundaries and different types of boundary conditions, as well as complex flow systems of two (or more) layers.