时变垂向入渗影响下河渠-潜水非稳定渗流模型的解及应用

在河渠边界控制下的半无限含水层中,对时变垂向入渗影响下的潜水非稳定渗流模型,利用Boussinesq第一线性化方法,通过Laplace变换并结合卷积原理,导出模型的解析解．根据不同水文地质条件下解的数学特征,建立相应的含水层参数求解方法;在此基础上,建立计算河渠与含水层之间水量交换的公式,以及计算潜水蒸发强度的递推公式．以安徽淮北平原某河流-潜水含水层系统为例,阐述上述方法的计算过程与步骤．     

河渠水位线性变化条件下河渠-潜水非稳定流模型及其解

在河渠水位迅速变化后再缓慢变化的条件下,建立了河渠半无限潜水含水层中非稳定渗流模型.利用Boussinesq第一线性化方法及Laplace变换,并注意应用Laplace变换中的"积分性质",给出形式相对简单、由常用函数表达的解,阐述特定解及其相应的物理意义.由解所揭示的潜水位变化规律表明,含水层任一点处潜水位变动速度的时间变化曲线形态是固定的,与河渠边界水位变动速率λ无关;潜水最大变速发生的时间,随λ呈非线性位移.依据潜水位变化规律,建立利用潜水位变动速度求含水层参数的方法,并用实例演示了拐点法求参数的过程.     

通用函数边界下潜水非稳定流模型的解及应用

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.     

潜水污染问题数学模型的广义解

讨论了具有混合边界的潜水污染数学模型，在适当条件下，应用Galerkjn方法证明了模型广义解的存在性，并证明了广义解的唯一性和对初边值及自由项的连续依赖性．     

推广的线性模型的参数估计

本文导出区间数变量和三角模糊变量的线性模型的参数公式．公式简单，形式一致，可作为经典线性回归模型参数估计最小二乘法推广。     

如何做实证:路径分析北大核心

在回归模型中,可以包括多个自变量,但只能包括一个因变量．而许多因果效应问题,因变量往往不止一个．回归分析还有一个局限就是只能分析直接效应,不能分析间接效应．事实上,许多变量之间可能有直接关系,也可能受到中介变量的影响而产生间接效应．路径分析就是解决这类问题的方法．     

矩形边界越流承压含水层中非完整井稳定流解析解

针对矩形边界越流承压含水层中非完整井抽水引起的复杂地下水流动问题,建立了直角坐标系下越流承压含水层非完整井稳定流数学模型.通过对地下水流动计算模型的有限Fourier变换和有限Fourier变换域降深函数的逆变换,提出了不同类型边界条件下越流承压含水层非完整井三维稳定流降深解析解.在验证降深解析解正确性的基础上,通过降深解析解计算精度的分析,并结合非完整井抽水条件下含水层地下水流动特性,给出了降深解析解满足计算精度要求的计算项数取值.探讨了含水层正交各向异性、抽水井完整性、井位布置等因素对含水层降深和地下水流动的影响规律,并利用工程案例阐明了降深解析解的工程适用性.     

第五类Painlevé方程解的渐近性态分析

本文用比较直接的方法研究Painleve方程的渐近解和连同公式:(1)先求出数值解,然后用最小二乘法拟合出最佳渐近解;(2)根据最佳渐近解的表达形式,用谐波平衡法得到振荡渐近解与参数之间的依赖关系,即连同公式．当参数α,β,γ和δ满足一些条件时,对一般实的第五类Painleve方程,我们找出了振荡渐近解和连同公式．     

组合证券投资的有效边界

本文讨论了由Ｍａｒｋｏｗｉｔｚ提出的证券组合模型的边界函数性质．并给出了在变量非负条件下边界函数的确定方法。得出了在非负条件下有效边界函数是预期回收值的逐段二次凸函数以及Ｍａｒｋｏｗｅｉｔｚ模型的最优解是预期回收值的逐段线性向量函数的结论。     

孔洞裂隙水二维流数值模拟的广义差分法

研究区地下水主要为玄武岩类孔洞裂隙水,水文地质模型概化为各向异性非均质,根据第四系玄武岩承压含水层中地下水的分布特征及流动规律,建立二维非稳定流数学模型,采用广义差分法对其求解.通过研究区井群对模型进行识别、验证.结果表明,计算模型与实际水文地质条件比较接近;计算水位与实测水位相吻合.为城市地下水可持续性管理提供科学理论依据.     

Steady Groundwater Flow with Steep Gradients: An Analytic Approach to the 2D–Problem with a Vertical Pressure Boundary Condition and Steady Recharge/Drainage

Steady groundwater flow with steep gradients in a vertical plane due to superficial recharge/drainage, inner sources/sinks and a one‐sided pressure boundary condition can be described by a 2D Poisson equation with a nonlinear free surface boundary condition. By means of conformal mapping techniques Schmitz and Edenhofer [1] derived the exact explicit solution of this problem in a horizontally infinite aquifer. Their results are extended to problems with a one‐sided vertical pressure boundary condition, modelling f. ex. the boundary between an aquifer and an adjacent free water body. According to ist simple parametrization, this approach can be applied on one hand to model various real world phenomena like river–aquifer–systems. It may on the other hand serve as a tool for investigating the exactness of numerical solutions and the range of validity of simplifying assumptions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary element solution of the two-dimensional groundwater flow equation with stochastic free surface boundary condition

An innovative approach to the approximate solution of stochastic partial differential equations in groundwater flow is presented. The method uses a formulation of the Ito's lemma in Hilbert spaces to derive partial differential equations satisfying the moments of the solution process. Since the moments equations are deterministic, they could be solved by any analytical or numerical method existing in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two-dimensional or three-dimensional domains of any geometrical shape. The method is tested for the first time in the present paper through a practical application in a sandy phreatic aquifer at the Chalk River Nuclear Laboratories, Ontario, Canada. The equation solved is the two-dimensional LaPlace equation with a dynamic, randomly perturbed, free surface boundary condition. The moments equations are derived and solved by using the boundary integral equation method. A comparison is made with a previous analytical solution obtained by applying the randomly forced one-dimensional Boussinesq equation, and some observations on modeling procedures are given.     

Groundwater response to tidal fluctuation in a sloping leaky aquifer system

The effect of tidal fluctuation on groundwater flow is an important issue from many aspects in coastal areas. This paper develops a new analytical solution to describe the groundwater fluctuation in a sloping coastal aquifer system which comprises an upper unconfined aquifer, a lower confined aquifer, and an aquitard in between. The solution is allowed to investigate the effects of bottom slope and leakage as well as aquifer parameters on head fluctuations in both unconfined and confined aquifers. The research result indicates that the effect of the bottom angle on the groundwater fluctuation and time lag is significant in the unconfined aquifer and not negligible if the leakage in the confined aquifer is large. In addition, the joint effects of aquifer parameters and bottom angle on groundwater fluctuation and time lag are also discussed.     

相似理论和泥沙的垂直分布

本文利用相似性原理处理了二维渠道均匀定常挟沙水流,在湍流脉动速度和含沙量涨落值相似的条件下,我们得到了泥沙垂直于挟沙水流的流动方向的含沙量分布.这个含沙量分布和扩散理论得到的含沙量分布略有差别,而和重力理论得到的含沙量分布则差别较大.     

Analytical solution for the evolution of exit point along the sloping seepage face

This paper developed an analytical solution for the problem of exit point evolution on the seepage face in the unconfined aquifer with sloping interface. A theoretical model for the groundwater drawdown problem in a half‐infinite aquifer with a sloping boundary is built in accordance with the linearized one‐dimensional Boussinesq equation and the Neumann boundary condition at the seepage point. The homotopy analysis method is then adopted for solving this dynamic boundary problem. By constructing two continuous deformations, the original problem could be converted into a group of subproblems with the same physical essence and similar mathematical solutions. To compare this analytical solution, a numerical model based on the finite volume method is developed, which employs adaptive grids to settle the dynamic boundary condition. The comparisons show that the analytical solution agrees with the numerical model well. The results are useful for the quantification of various hydrological problems. The methodology applied in this study is referential for other dynamic boundary problems as well.     

直立圆柱二阶波浪力解析解

大直径直立圆柱体上的二阶波浪力目前已有一些研究结果,但仍存在一些值得进一步探讨之处.这一方面在于二阶辐射条件还不甚清楚:另一方面在于已有的二阶力公式或是所含积分的收敛精度不易保证,或是表达式繁杂,不利于实际计算.本文在求解这一问题时,不是对二阶势提出辐射条件,而是对二阶势的周向富里叶分量提出辐射条件──Sommerfeld辐射条件.求解中,利用本文推导出的数学公式,简化了二阶自由面条件非齐次项的表达式,得到了形式简单,易于计算的二阶波浪力精确公式.二阶力计算结果与实验结果吻合良好.     

Saturated-unsaturated flow in a fractured unconfined aquifer

Saturated-unsaturated flow is investigated in an unconfined aquifer containing a distribution of fractures such that on some macroscopic scale there can be defined a smooth averaged hydraulic conductivity. After constructing the conditions which relate the hydraulic properties between the unsaturated and saturated zones, it is shown that the flow in the unsaturated zone is essentially vertical. Below the water table the macropores are conduits for groundwater and the flow has a large horizontal component. Some important implications on previous models is discussed.     

Application of Nelder-Mead simplex method for unconfined seepage problems

In unconfined seepage problems, the phreatic line resulted from mesh deforming methods is rarely a smooth and continuous curve. The main problem is at the meeting point of the phreatic line with the down stream face of the dam where the phreatic line must be tangent to the seepage face according to the fluid continuity principle. In this paper a mesh deforming finite element method based on Nelder-Mead simplex optimization is presented to solve this problem. The phreatic line is approximated by a 4th degree polynomial and Nelder-Mead simplex method is used to calculate the polynomial’s coefficients minimizing an error function which is introduced based on the conditions on the phreatic line. Tangentiality of the phreatic line to the seepage face is introduced in the solution by a constraint in optimization procedure. The results of the presented method are verified by the results of the nonlinear finite element and other mesh deforming methods.     

Study of free convective boundary layer of isothermal lateral surface of axisymmetrical horizontal body

Approximate analytical solution of simplified Navier–Stokes and Fourier–Kirchhoff equations describing free convective heat transfer from isothermal surface has been presented. It is supposed that the surface has the horizontal axis of symmetry and its axial cross-section lateral boundary is a concave function. The equation for the boundary layer thickness is derived for typical for natural convection assumptions. The most important are that the convective fluid flow is stationary and the normal to the surface component of velocity is negligibly small in comparison with the tangential one. The theoretical results are verified by two characteristic cases of the revolution surfaces namely for horizontal conic and vertical round plate. Both limits of presented solution coincide with known formulas.