中文摘要：

现有地下水半解析数值方法不能应用于潜水含水层的地下水流问题。为此,基于Neuman模型提出了潜水非稳定流的半解析数值求解格式,利用伽辽金法与正交解析函数族推导了解耦形式的加权余量方程式。在编制Fortran计算程序实现数值求解的基础上,利用已有解析解验证了方法及程序的正确性,计算结果很好地反映了潜水完整井流具有的三维流动特性及潜水面滞后反应效应,而且当忽略给水度时,该方法可以退化为针对承压含水系统的已有成果。数值算例表明,半解析数值方法适用于模拟包括潜水含水层、承压含水层及弱透水层的多层结构含水层系统的地下水流问题,能够为可概化成层状含水系统的地下水开采及地面沉降等问题中三维水流模型的高效计算提供途径。

英文摘要：

The existing semi-analytical numerical method can not be used to simulate unconfined flow of groundwater. Therefore, a semi-analytical numerical approach for the problems of unsteady groundwater flow in unconfined aquifers is proposed by using the Nueman＇s model for the response of the water table, and the decoupled weighted residual equations are derived by means of the Galerkin＇s method and the orthogonality of the trigonometric series. A computer program is developed for the semi-analytical numerical analysis of three-dimensional groundwater flow in unconfined aquifers, and the validities of the present method and program are verified by comparisons with the existing analytical solutions. The three-dimensional pattern of unconfined flow due to a fully penetrating well and the delayed response of the water table are studied based on the numerical results. Moreover, the proposed method can be reduced to the existing method for confined flow if the specific yield of unconfined aquifers is ignored. Finally, the applicability of the semi-analytical numerical method for simulating the three-dimensional flow in the aquifer systems consisting of an unconfined aquifer, an aquitard and a confined aquifer is demonstrated through an additional numerical application. The proposed method can provide a high efficient approach for the three-dimensional simulation of groundwater flow and land subsidence due to groundwater withdrawal in layered aquifer systems.