复杂函数边界控制下的潜水非稳定流模型及解的应用  

Application of unsteady phreatic flow model and its solution under the boundary control of complicated function

作　　者：吴丹[1] 陶月赞[1] 林飞[1] WU Dan;TAO Yuezan;LIN Fei(School of Civil Engineering,Hefei University of Technology,Hefei 230009,Chin)

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009

出　　处：《水利学报》2018年第6期725-731,共7页Journal of Hydraulic Engineering

基　　金：国家自然科学基金项目(51509064)

摘　　要：为解决复杂河渠水位边界影响下的潜水非稳定流模型难以求解的问题,建立不依赖边界函数的变换过程的Fourier变换方法,利用卷积定义和卷积的微分性质,给出模型的理论解;对实际河渠水位过程采用Lagrange线性插值,将插值函数代入理论解,可简便地获得问题的实际解。研究表明:(1)该方法求解过程比较简明,且解是由形式较简单的常用函数组成;(2)依据潜水位变动速度的时间过程计算模型参数的配线法,方法简便;(3)边界水位变化过程,对河渠与潜水之间的水量交换作用,有2倍于边界水位变幅的累积效应。Based on the Fourier transformation,a method independent on the transformation process is pro-posed to solve the phreatic unsteady flow model controlled by the complex canal-water-level boundary. Thetheoretical solution of the model is given by using the convolution definition and the differential property ofthe convolution. Lagrange linear interpolation is applied to the actual water level process,and the interpola-tion function is substituted into the theoretical solution,and the actual solution of the problem can be ob-tained easily. The results show that：（1） The method is relatively simple and the solution is composed ofcommon functions with simpler forms;（2） The wiring method for calculating the parameters of the modelbased on the time course of the fluctuating speed of phreatic level is simple and convenient;（3） Theboundary water level change process has a cumulative effect of two times the amplitude of the boundary wa-ter level in the exchange of water between the canal and phreatic water.

关 键 词：潜水非稳定流 LAGRANGE插值 FOURIER变换 卷积微分性质 累积效应 

分 类 号：P641.132[天文地球—地质矿产勘探]