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   

The similitude equation in magnetotelluric inversion     

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

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Analysis of mapping coverage obtained from spacecraft     

Anastassios E. Petropoulos  James M. Longuski 《Celestial Mechanics and Dynamical Astronomy》1994,60(4):431-454

An exact analysis of the coverage obtained by spacecraft using cross-track scanning and nadir-centered conical imaging, under imposed viewing obliqueness and resolution requirements, is presented. In addition to exact expressions for the area acquired and the area acquisition rate, envelope theory is introduced to obtain the boundary of the imaged area. These expressions are relatively compact, allowing rapid machine computation. The effects of the sun phase angle, and of imaging system limitations are also examined. The Galileo mission encounter with Callisto is used as a numerical example, from which certain general conclusions are drawn regarding optimal imaging trajectories.  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

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Transforming observational data and theoretical isochrones into the ACS/WFC Vega-mag system     

Luigi R. Bedin †  Santi Cassisi  Fiorella Castelli  Giampaolo Piotto  Jay Anderson  Maurizio Salaris  Yazan Momany  Adriano Pietrinferni 《Monthly notices of the Royal Astronomical Society》2005,357(3):1038-1048

We propose a zero-point photometric calibration of the data from the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) on board the Hubble Space Telescope , based on a spectrum of Vega and the most up-to-date in-flight transmission curves of the camera. This calibration is accurate at the level of a few hundredths of a magnitude. The main purpose of this effort is to transform the entire set of evolutionary models into a simple observational photometric system for ACS/WFC data, and to make them available to the astronomical community. We provide the zero-points for the most used ACS/WFC bands, and give basic recipes for calibrating both the observed data and the models. We also present the colour–magnitude diagram from ACS data of five Galactic globular clusters, spanning the metallicity range  −2.2 <[Fe/H] < −0.04  , and we provide fiducial points representing their sequences from several magnitudes below the turn-off to the red giant branch tip. The observed sequences are compared with the models in the newly defined photometric system.  相似文献