复杂函数边界控制下的潜水非稳定流模型及解的应用
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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.
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.
引文
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[10]陶月赞,曹彭强,席道瑛.垂向入渗与河渠边界影响下潜水非稳定流参数的求解[J].水利学报,2006,37(8):913-917.
[11]ALI Mahdavi.Transient-State analytical solution for groundwater recharge in anisotropic sloping aquifer[J].Water Resources Management,2015,29(10):3735-3748.
[12]TANG Y H,JIANG Q H,ZHOU C B.Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary[J].Water Resources Reseach,2016,52(4):2529-2550.
[13]SU N H.The fractional Boussinesq equation of groundwater flow and its applications[J].Journal of Hydrology,2017,547(2):403-412.
[14]BANSAL R K.Approximation of surface-groundwater interaction mediated by vertical stream bank in sloping terrains[J].Journal of Ocean Engineering and Science,2017,2(1):18-27.
[15]闵琦.δ函数的定义及其性质[J].大学物理,2004,23(9):18-20.
[16]滕岩梅.积分变换中常见问题[J].大学数学,2015,31(1):105-109.
[2]BEAR J.多孔介质流体力学[M].李竞生,陈崇希,译.北京:中国建筑工业出版社,1983.
[3]DAVID K T,LARRY W M.Groundwater Hydrology[M].3rd ed.John Wiley&Sons Inc.,2005.
[4]SERGIO E S.Modelling groundwater flow under transient nonlinear free surface[J].Journal of Hydrologic Engineering,2003,8(3):123-132.
[5]李山,罗纨,贾忠华,等.半湿润灌区控制排水条件下降雨洗盐计算模型研究[J].水利学报,2015,46(2):127-137.
[6]彭振阳,伍靖伟,黄介生.内蒙古河套灌区局部秋浇条件下农田水盐运动特征分析[J].水利学报,2016,47(1):110-118.
[7]SRIVASTAVA K,SERRANO S E,WORKMAN S R.Stochastic modeling of transient stream-aquifer interaction with the nonlinear Boussinesq equation[J].Journal of hydrology,2006,328(3/4):538-547.
[8]LIANG X Y,ZHANG Y K.Temporal and spatial variation and scaling of groundwater levels in a bounded unconfined aquifer[J].Journal of hydrology,2013,479(1/2):139-145.
[9]TAO Y Z,YAO M,ZHANG B F.Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage[J].Applied Mathematics and Mechanics,2007,28(9):1173-1180.
[10]陶月赞,曹彭强,席道瑛.垂向入渗与河渠边界影响下潜水非稳定流参数的求解[J].水利学报,2006,37(8):913-917.
[11]ALI Mahdavi.Transient-State analytical solution for groundwater recharge in anisotropic sloping aquifer[J].Water Resources Management,2015,29(10):3735-3748.
[12]TANG Y H,JIANG Q H,ZHOU C B.Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary[J].Water Resources Reseach,2016,52(4):2529-2550.
[13]SU N H.The fractional Boussinesq equation of groundwater flow and its applications[J].Journal of Hydrology,2017,547(2):403-412.
[14]BANSAL R K.Approximation of surface-groundwater interaction mediated by vertical stream bank in sloping terrains[J].Journal of Ocean Engineering and Science,2017,2(1):18-27.
[15]闵琦.δ函数的定义及其性质[J].大学物理,2004,23(9):18-20.
[16]滕岩梅.积分变换中常见问题[J].大学数学,2015,31(1):105-109.