通用函数边界下潜水非稳定流模型的解及应用

刘能胜; 曹恒明

doi:10.21656/1000-0887.400371

通用函数边界下潜水非稳定流模型的解及应用

doi: 10.21656/1000-0887.400371

刘能胜¹,
曹恒明²

¹湖北水利水电职业技术学院, 武汉 430070;²盐城市图书馆, 江苏盐城 224005

详细信息

作者简介:
刘能胜（1979—），男，副教授，硕士（通讯作者. E-mail: 7367428@qq.com）.

中图分类号: P641.132
计量
- 文章访问数: 3139
- HTML全文浏览量: 254
- PDF下载量: 321
- 被引次数: 0
出版历程
- 收稿日期: 2019-12-12
- 修回日期: 2020-03-09
- 刊出日期: 2020-09-01

Solution and Application of the Transient Phreatic Flow Motion Model Under General Function Boundary

LIU Nengsheng¹,
CAO Hengming²

¹Hubei Water Resources Technical College, Wuhan 430070, P.R.China;²Yancheng Library, Yancheng, Jiangsu 224005, P.R.China

摘要

摘要: 针对半无限域河渠附近潜水非稳定运动经典模型中河渠水位边界条件概化的局限性，在经典模型的基础之上将河渠水位变化过程概化为通用函数形式，并采用Laplace变换方法对模型进行处理，结合Laplace变换中的微分定理和卷积定理，给出了模型的解析解.同时，为探讨解在实际问题中的运用，对河渠水位变化过程进行Lagrange线性插值，并结合相关实测水位数据，利用MATLAB软件对含水层参数进行求解.结果表明，通用函数形式河渠水位边界条件下给出的模型解析式形式较为简洁，解的构成也均为常规函数，结合插值函数，经处理后进行含水层参数求解，方法简便且结果精度较高，具有较好的推广价值.
- 潜水非稳定流 /
- Laplace变换 /
- Lagrange插值 /
- MATLAB
Abstract: In view of the limitations on the generalization of the canal water level boundary conditions for the classic transient phreatic flow motion model near the semi-infinite domain canal, and based on this model, the water level change process of the canal was generalized into a general function form, and the Laplace transform method was used to process the model. Combined with the differential theorem and convolution theorem in the Laplace transform, the analytical solution of the model was given. To explore the application of the solution to practical problems, the water level change process of the canal was analyzed by the Lagrange interpolation, and the MATLAB software was used to solve the aquifer parameters with the relevant measured water level data. The results show that, the analytic general function form model under the river channel water level boundary conditions is relatively simple, and the composition of the solution includes all conventional functions. Combined with the interpolation functions, the proposed model works well in solution of the aquifer parameters with high precision and apparent simplicity, and has good popularization values.
- transient phreatic flow /
- Laplace transform /
- Lagrange interpolation /
- MATLAB

HTML全文

参考文献(19)

[1]	张蔚榛. 地下水非稳定流计算和地下水资源评价[M]. 北京: 科学出版社, 1983.(ZHANG Weizhen. Calculation of Unsteady Flow of Groundwater and Evaluation of Groundwater Resources [M]. Beijing: Science Press, 1983.(in Chinese))
[2]	沙金煊. 农田不稳定排水理论与计算[M]. 北京: 中国水利水电出版社, 2004.(SHA Jinxuan. Theory and Calculation of Unsteady Drainage in Farmland [M]. Beijing: China Water & Power Press, 2004.(in Chinese))
[3]	薛禹群. 地下水动力学[M]. 北京: 地质出版社, 2010.(XUE Yuqun. Dynamics of Groundwater [M]. Beijing: Geological Publishing House, 2010.(in Chinese))
[4]	瞿兴业. 农田排灌渗流计算及其应用[M]. 北京: 中国水利水电出版社, 2011.(QU Xingye. Calculation and Application of Drainage and Irrigation Seepage in Farmland [M]. Beijing: China Water & Power Press, 2011.(in Chinese))
[5]	贾志峰, 李文宾, 贾志锐. 潜水非稳定渗流边界条件处理方法研究[J]. 灌溉排水学报, 2013,32(3): 44-49.(JIA Zhifeng, LI Wenbin, JIA Zhirui. Boundary conditions treatment method in un-confined unsteady flow seepage process[J]. Journal of Irrigation and Drainage,2013,32(3): 44-49.(in Chinese))
[6]	张鸿雁. 河渠水位曲线回水影响半无限含水层河渠附近地下水非稳定流计算[J]. 长春地质学院学报, 1987,17(3): 319-330.(ZHANG Hongyan. Unsteady groundwater flow calculation in a semi-infinite aquifer near a river or channel affected by backwater level in the river or channel[J]. Journal of Changchun College of Geology,1987,17(3): 319-330.(in Chinese))
[7]	阿里木·吐尔逊, 周志芳, 木塔力甫·依明尼亚孜. 河渠附近潜水非稳定运动的一种通解[J]. 河海大学学报(自然科学版), 2003,31(6): 649-651.(ALIM Tursun, ZHOU Zhifang, MUTALIP Iminniyaz. A universal solution to unstable groundwater movement in vicinity of canals[J]. Journal of Hohai University(Natural Sciences),2003,31(6): 649-651.(in Chinese))
[8]	杨红坡, 谢新宇, 张继发, 等. 潜水一维非稳态运动的解析理论及应用[J]. 水科学进展, 2004 ,15(1): 82-86.(YANG Hongpo, XIE Xinyu, ZHANG Jifa, et al. Analytical solution of one-dimensional transient phreatic flow and its application[J]. Advances in Water Science,2004,15(1): 82-86.(in Chinese))
[9]	陶月赞, 席道瑛. 垂直与水平渗透作用下潜水非稳定渗流运动规律[J]. 应用数学和力学, 2006,27(1): 53-59.(TAO Yuezan, XI Daoying. Rule of transient phreatic flow subjected to vertical and horizontal seepage[J]. Applied Mathematics and Mechanics,2006,27(1): 53-59.(in Chinese))
[10]	LIANG X Y, ZHANG Y K. Analytic solutions to transient groundwater flow under time-dependent sources in a heterogeneous aquifer bounded by fluctuating river stage[J]. Advances in Water Resources,2013,8(58): 1-9.
[11]	MAHDAVI A. Transient-state analytical solution for groundwater recharge in anisotropic sloping aquifer[J]. Water Resources Management,2015,29(10): 1-14.
[12]	YOUNGS E G, RUSHTON K R. Dupuit-Forchheimer analyses of steady-state water-table heights due to accretion in drained lands overlying undulating sloping impermeable beds[J]. Journal of Irrigation and Drainage Engineering,2009,135(4): 467-473.
[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]	张建锋, 李国敏, 张元, 等. 塔河下游间歇性输水河道附近地下水位动态响应[J]. 地球物理学报, 2012,55(2): 622-630 .(ZHANG Jianfeng, LI Guomin, ZHANG Yuan, et al. Responses of groundwater levels to intermittent water transfer in the lower Tarim River[J]. Chinese Journal of Geophysics,2012,55(2): 622-630 .(in Chinese))
[16]	张学宏, 李颜, 郝培章, 等. 水文资料插值计算方法探讨[J]. 海洋预报, 2008,25(1): 5-13.(ZHANG Xuehong, LI Yan, HAO Peizhang, et al. Discussion on the interpolation calculation methods of hydrological data[J]. Marine Forecasts,2008,25(1): 5-13.(in Chinese))
[17]	吴丹, 陶月赞, 林飞. 河渠水位线性变化条件下河渠-潜水非稳定流模型及其解[J]. 应用数学和力学, 2018,39(9): 1043-1050.(WU Dan, TAO Yuezan, LIN Fei. Solution of the transient stream-groundwater model with linearly varying stream water levels[J]. Applied Mathematics and Mechanics,2018,39(9): 1043-1050.(in Chinese))
[18]	吴丹, 陶月赞, 林飞. 复杂函数边界控制下的潜水非稳定流模型及解的应用[J]. 水利学报, 2018,〖STHZ〗 49(6): 725-731.(WU Dan, TAO Yuezan, LIN Fei. Application of unsteady phreatic flow model and its solution under the boundary control of complicated function[J]. Journal of Hydraulic Engineering,2018,49(6): 725-731.(in Chinese))
[19]	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,〖STHZ〗 37(8): 913-917.(TAO Yuezan, CAO Pengqiang, XI Daoying. Parameter estimation for semi-infinite phreatic aquifer subjected to vertical seepage and bounded by channel[J]. Journal of Hydraulic Engineering,2006,〖STHZ〗 37(8): 913-917.(in Chinese))