Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation          下载免费PDF全文

Tongbi Tu  Ali Ercan  M. Levent Kavvas 《水文研究》2018,32(10):1406-1419

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.  相似文献   

有关边界层问题中一类奇异积分方程新的存在性结果     

石丽莉  张高勋 《成都信息工程学院学报》2006,21(6):891-896

对边界层理论新结果中出现的一类奇异积分方程w（t）=∫1 t（1-s）（λ＋λs＋s）/w（s）ds＋（1-t）∫t 0s/w（s）ds,t∈（0,1）进行讨论，并得出了上述方程在λ∈（-1/2,0）上正解存在性的新结果。  相似文献   

关于Diophantine方程的解     

乐茂华 《广东海洋大学学报》2004,24(4):47-48

对于正整数a ,设S(a)是Smarandache函数。证明了 :方程S(1·2 ) +S(2·3) +… +S(x(x +1) ) =S(x(x +1) (x +2 ) /3)仅有正整数解x =1。  相似文献   

用比电导法研究活性炭的吸附特性     

陈以良 《广东海洋大学学报》1992,(1)

用比电导法研究两种活性炭自稀水溶液中吸附强电解质硫酸铬和硫酸铜的吸附平衡特性。结果表明,在本文的研究条件下,两种活性炭对硫酸铬和硫酸铜都有吸附作用。同时,活性炭吸附硫酸铜的吸附平衡特性可以用 Freundlich 方程式来描述。研究的结果对固体在溶液中的吸附基础理论以及处理工业废水具有一定的意义。  相似文献   

Simulation of adaptive optics for the Vacuum Tower Telescope     

Anita Enmark  Thomas Berkefeld  Oskar von der Lühe  Torben Andersen 《Experimental Astronomy》2006,21(2):87-99

A simulation model of the adaptive optics of the German Vacuum Tower Telescope (VTT), Observatorio del Teide, Tenerife, is presented. The model uses modules from the integrated model of the Euro50 extremely large telescope, and includes submodels of a Shack-Hartmann wavefront sensor, a de-formable mirror, a tip-tilt mirror, high-voltage amplifier low-pass filters, a reconstructor and a controller. We investigate the impact on the closed loop bandwidth of changes in controller configuration and certain system parameters, such as low pass filter bandwidth and camera integration and readout time. Control strategies were tested on simple models before implementation on the full VTT model. Using the models, different control strategies are compared.  相似文献   

The similitude equation in magnetotelluric inversion     

S. E. Dosso  D. W. Oldenburg 《Geophysical Journal International》1991,106(2):507-509

  相似文献   

Numerical prediction of blast‐induced stress wave from large‐scale underground explosion     

Chengqing Wu  Yong Lu  Hong Hao 《国际地质力学数值与分析法杂志》2004,28(1):93-109

This paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

非线性Rossby波所满足的三阶Zakharov方程与低频振荡     

罗德海 《成都信息工程学院学报》1993,(4)

本文在基本气流具有水平切变的情况下,利用摄动法导出了非线性Rossby波所满足的三阶Zakharov方程,然后,考虑了基流具有弱切变的情况,通过使用三阶Zakharov方程研究了Rossby波列的第一类不稳定性问题。结果表明:通过非线性作用,大气中的Rossby波列可产生调制不稳定。同时,本文对这种不稳定的区域,增长率和周期进行了详细的计算,并讨论了波振幅、波数、纬度和基流切变对它们的影响,指出Rossby波列的调制不稳定可以激发30～60天的低频振荡。  相似文献   

Viscoelastodynamics of A Stratified, Compressible Planet: Incremental Field Equations and Short- and Long-Time Asymptotes     

Detlef Wolf 《Geophysical Journal International》1991,104(2):401-417

  相似文献   

Obtaining basic simulation data for a heterogeneous field with stratified marine soils     

P. A. Finke  W. J. P. Bosma 《水文研究》1993,7(1):63-75

Thinly stratified sedimentary deposits in a heterogeneous field were investigated to obtain basic physical data for the simulation of water flow. A procedure is described which translates a thinly stratified soil profile into a number of functional layers using functional hydrological properties. A functional layer is defined as a combination of one or more soil horizons and should (i) be recognizable during a soil survey using an auger and (ii) show significantly different functional hydrological properties when compared with another functional layer. This procedure gave three easily recognizable functional layers. Sets of hydrological characteristics of these three functional layers were obtained by physical measurements of the soil and by estimation, using textural data for classification into a standard Dutch series. The performance of several combinations of these sets was tested by comparing simulated and measured soil matric potentials for seven plots during one year. The best simulation results were obtained if measured soil hydraulic characteristics were used for relatively homogeneous functional layers and if the soil hydraulic characteristics were estimated at each location for the most heterogeneous layer.  相似文献