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1.
Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation 下载免费PDF全文
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
2.
Janis Britals 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):305-316
It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy. 相似文献
3.
Christopher Kotsakis 《Journal of Geodesy》2009,83(1):31-50
All gravity field functionals obtained from an Earth gravitational model (EGM) depend on the underlying terrestrial reference
frame (TRF), with respect to which the EGM’s spherical harmonic coefficients refer to. In order to maintain a coherent framework
for the comparison of current and future EGMs, it is thus important to investigate the consistency of their inherent TRFs,
especially when their use is intended for high precision studies. Following the methodology described in an earlier paper
by Kleusberg (1980), the similarity transformation parameters between the associated reference frames for several EGMs (including
the most recent CHAMP/GRACE models at the time of writing this paper) are estimated in the present study. Specifically, the
differences between the spherical harmonic coefficients for various pairs of EGMs are parameterized through a 3D-similarity
spatial transformation model that relates their underlying TRFs. From the least-squares adjustment of such a parametric model,
the origin, orientation and scale stability between the EGMs’ reference frames can be identified by estimating their corresponding
translation, rotation and scale factor parameters. Various aspects of the estimation procedure and its results are highlighted
in the paper, including data weighting schemes, the sensitivity of the results with respect to the selected harmonic spectral
band, the correlation structure and precision level of the estimated transformation parameters, the effect of the estimated
differences of the EGMs’ reference frames on their height anomaly signal, and the overall feasibility of Kleusberg’s formulae
for the assessment of TRF inconsistencies among global geopotential models. 相似文献
4.
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
5.
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
6.
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
7.
8.
Numerical methods are usually used for the computation of ephemerides with perturbations for the precise orbital determination of an artificial satellite. But their numerical stability will be encountered in a long arc. In this case the use the improved Encke special perturbation methods has been suggested. The results of this paper show that Encke's method does indeed have a certain effectiveness, but cannot yet completely resolve the numerical stability, and the more efficient method is to use the energy integral or its variational relation to control the growth of the along-track error in general numerical calculations so that the aim of stabilization can be achieved. 相似文献
9.
10.
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