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1.
Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation
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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.
A constitutive relation is derived for describing the mechanical response of chalk. The approach is based on a phenomenological framework which employs chemo‐plasticity. The properties of the material are assumed to be affected by the physico‐chemical processes that occur through the interaction between the skeleton and the pore fluid. The underlying mechanism is discussed by invoking a micromechanical analysis. The performance of the framework is illustrated by examining the evolution of mechanical characteristics in the presence of different pore fluids. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
3.
在常规照相天体测量工作中 ,对暗天体的定位是采用逐级定标星过渡的方法实现的。由于星表系统差和局部差的存在 ,最终定位结果可能包含难以把握的误差积累。在CCD小视场观测情况下时常难以找到足够数量的定标星。鉴于此 ,推导了CCD观测联合平差方法的严格矢量表达式 ,以期通过共同星的过渡 ,实现大天区统一平差。原理上此方法可实现相对于河外天体的定位 ,以削弱星表系统差和局部差对定位结果的影响。讨论了CCD联合平差方法实现中的问题 ,包括底片常数模型选择、切点位置改正、共同星的较差改正和法方程解算方法等 ,并分析了具体的处理措施。用实例初步检验了CCD联合平差方法的效果 ,表明通过对多张CCD观测的联合平差 ,可以削弱单张CCD观测参考星数目过少、单张CCD观测参考星分布不均、个别参考星存在位置偏差和局部区域参考星存在系统性位置偏差等不利因素对归算结果的影响 ,进而达到扩大视场和提高归算精度的目的 相似文献
4.
This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x
0 ∊ [−2,2],C ∊ [−2,5]) of the (x
0, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x
0 ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order
n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x
0, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D
i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families. 相似文献
5.
A modified method of mine tremors location used in Lubin Copper Mine is presented in the paper. In mines where an intensive exploration is carried out a high accuracy source location technique is usually required. The effect of the flatness of the geophones array, complex geological structure of the rock mass and intense exploitation make the location results ambiguous in such mines. In the present paper an effective method of source location and location's error evaluations are presented, combining data from two different arrays of geophones. The first consists of uniaxial geophones spaced in the whole mine area. The second is installed in one of the mining panels and consists of triaxial geophones. The usage of the data obtained from triaxial geophones allows to increase the hypocenter vertical coordinate precision. The presented two-step location procedure combines standard location methods: P-waves directions and P-waves arrival times. Using computer simulations the efficiency of the created algorithm was tested. The designed algorithm is fully non-linear and was tested on the multilayered rock mass model of the Lubin Copper Mine, showing a computational better efficiency than the traditional P-wave arrival times location algorithm. In this paper we present the complete procedure that effectively solves the non-linear location problems, i.e. the mine tremor location and measurement of the error propagation. 相似文献
6.
传统的Poulos弹性理论仅适合于均质土中土体侧向位移时桩的性状分析,无法考虑土的层状特性。通过引入层状地基中作用一水平集中力的广义Mindlin解和地面作用有竖向荷载时的应力和位移通解,对Poulos方法进行了改进,使之扩展到多层土中,还用于研究堆载条件下的被动桩变形和受力响应。算例分析表明,改进弹性理论要比Poulos方法更为严密、合理,提高了计算精度,应用范围也更广。 相似文献
7.
In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement. 相似文献
8.
水溶液中聚合物在粘土上的吸附对于聚合物污染防治和污水处理等都有重要意义。Scheutjens-Fleer理论是应用范围最广的聚合物吸附理论,适应于从单体到长链高聚物,从链无相互作用的稀溶液到纯聚合物的吸附研究。本文简要介绍了有关聚合物吸附的重要参数,包括吸附量、耦合分数或直接表面覆盖、平均层厚度和链段密度,以及相应的测定方法。文中分析了影响聚合物吸附研究发展的主要问题,指出水溶液中聚合物在粘土上的吸附研究的发展方向是综合研究吸附等温线和A/V效应、耦合分数、吸附层厚度、吸附分级现象和对粘土层间的影响,并与Scheutjens-Fleer理论计算结果进行比较。 相似文献
9.
Experiments carried out with models of floating production, storage and offloading platforms (FPSOs) showed that the flow of water over the deck edge, onto the deck resembled a suddenly released wall of water rather than a breaking wave. Therefore green water flow onto the deck was simulated using dam breaking theory, but the theory’s shallow-water assumptions may be limiting. In this paper a non-linear dam breaking problem is formulated. Equations of motion in the Lagrangian form are used and the solution is sought as an infinite series in time. Comparisons with the shallow water approximation are carried out. 相似文献
10.
Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach 总被引:1,自引:0,他引:1
Computational Fluid Dynamic (CFD) based on Reynolds Averaged Navier–Stokes equation is used for determining the transverse hydrodynamic damping force and moment coefficients that are needed in the maneuverability study of marine vehicles. Computations are performed for two geometrical shapes representing typical AUVs presently in use. Results are compared with available data on similar geometries and from some of the available semi-empirical relations. It is found that the CFD predictions compares reasonable well with these results. In particular, the CFD predictions of forces and moments are found to be nonlinear with respect to the transverse velocity, and therefore both linear and nonlinear coefficients can be derived. A discussion on the sources of the component forces reveal that the total force and moment variations should in fact be nonlinear. 相似文献