垂直与水平渗透作用下潜水非稳定渗流运动规律

对河渠边界控制的半无限含水层,建立垂向入渗与河渠水平渗透共同作用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,给出模型的解析解. 证明相关经典公式与模型特定解之间的转换关系,分析经典公式适用范围．根据模型解,逐一定量研究下述变量,如垂向入渗强度、河渠水位变动幅度、含水层结构参数如给水度和导压系数、计算点与边界之间的距离,对渗流过程的影响．这些变量的变化,对潜水位获最大上升速度的时间产生延迟效应;论证一些变量间产生等效延迟效应的条件．根据解的数学特征,讨论其对应的物理意义和潜水位变动规律．     

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．     

二维潜水运动方程的分裂解法

本文通过对二维潜水运动方程的变形，按其在形式上所代表的意义不同，用和分裂方法，把它分解成“对流”和“扩散”两部分．对前者，用交替方向有限差分法求解；对后者，用交替方向Ｐｉｃａｒｄ迭代法进行计算，从而达到获得整个问题的解的目的．最后，用数值例子验证了所提方法的有效性，并与线性化的有限差分法作了对比，证明本文所提方法在计算精度上有所提高。     

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.     

多角度处理分装模型的计数与概率计算

从多个角度利用多种方法计算一类分装模型的计数,同时给出了相应的概率计算.分装模型就是将n个球分装到m个盒子中计数的模型.分装模型涉及到排列与组合、反演公式、容斥原理、Stirling数、生成函数及整数的分拆等组合数学中的大部分的计数方法.本文从组合数学的不同计数方法入手,详细叙述分装模型在不同情形下的解,深入剖析不同情形下解不同的原因.     

非线性Black-Scholes模型下阶梯期权定价

在非线性Black-Scholes模型下,研究了阶梯期权定价问题.首先利用多尺度方法,将阶梯期权适合的偏微分方程分解成一系列常系数抛物方程;其次通过计算这些常系数抛物型方程的解,给出了修正障碍期权的近似定价公式;最后利用Feymann-Kac公式分析了近似结论的误差估计.     

计算广义逆A_（T，S）~（1，2）和A_（T，S）~（2）的投影法及其应用

本文讨论投影法计算广义逆和，同时利用该方法解线性方程组得到了一些常用的迭代公式．     

一反应扩散模型解的有限元方法和误差分析

１引言在地下水运移过程中,污染物（溶质）随地下水在含水层中运移,并常常发生各种化学反应．文献［１－３］等提出并论述了三种化学物质（如Ｍ１,Ｍ２和Ｍ３）之间发生的一类化学反应．文献［４,５］等建立和描述了这类反应的数学模型（Ｐ）．文献［６,７」的作者首次对模型（Ｐ）进行了理论上的定性分析,主要是利用上,下解方法,算子半群理论和Ｓｏｂｏｌｅｖ空间的般人定理等论证了模型（Ｐ）的整体古典解的存在唯一性和渐近性质,文［６,７］也讨论了整体解的极限性态和收敛性估计．此外,文［８,９］等也就模型（Ｐ）的一类特…     

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.     

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.     

The Interface Between Fresh and Salt Groundwater: A Numerical Study

Present address: Laboratoire National d'Hydraulique, 6 quai Watier 78401 Chatou, France. In this paper the two-dimensional flow of fresh and salt waterthrough a homogeneous aquifer is considered. The two fluidsare assumed to be separated by a sharp interface. They differonly in their specific weight. This difference induces a flowin the aquifer which in turn causes a motion of the interface. We present a mathematical formulation of this problem whichconsists of a Poisson equation for the stream function coupledto a time evolution equation for the moving interface. The equationfor the stream function is solved by means of a finite-elementmethod while a predictor-corrector method (the S^ßscheme) is used for the discretization of the equation for theinterface.     

A High-Order Kernel-Free Boundary Integral Method for Incompressible Flow Equations in Two Space Dimensions

This paper presents a fourth-order kernel-free boundary integral method for the time-dependent, incompressible Stokes and Navier-Stokes equations defined on irregular bounded domains. By the stream function-vorticity formulation, the incompressible flow equations are interpreted as vorticity evolution equations. Time discretization methods for the evolution equations lead to a modified Helmholtz equation for the vorticity, or alternatively, a modified biharmonic equation for the stream function with two clamped boundary conditions. The resulting fourth-order elliptic boundary value problem is solved by a fourth-order kernel-free boundary integral method, with which integrals in the reformulated boundary integral equation are evaluated by solving corresponding equivalent interface problems, regardless of the exact expression of the involved Green's function. To solve the unsteady Stokes equations, a four-stage composite backward differential formula of the same order accuracy is employed for time integration. For the Navier-Stokes equations, a three-stage third-order semi-implicit Runge-Kutta method is utilized to guarantee the global numerical solution has at least third-order convergence rate. Numerical results for the unsteady Stokes equations and the Navier-Stokes equations are presented to validate efficiency and accuracy of the proposed method.     

Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data

We present methods to handle error-in-variables models. Kernel-based likelihood score estimating equation methods are developed for estimating conditional density parameters. In particular, a semiparametric likelihood method is proposed for sufficiently using the information in the data. The asymptotic distribution theory is derived. Small sample simulations and a real data set are used to illustrate the proposed estimation methods.     

Coefficients of Runge‐Kutta Schemes for Itô Stochastic Differential Equations

In order to approximate the solution of an Itô stochastic differential equation, embedded explicit stochastic Runge‐Kutta methods may be applied. Coefficients for such schemes are presented in this paper. Since embedded methods provide different orders of convergence, they may be applied for estimating the local error of the approximation process.     

A stationary flow of fresh and salt groundwater in a coastal aquifer with nonlinear darcy' law

We study an homogeneous aquifer where fresh and salt water are separated by an interface T. The flow is governed by a nonlinear Darcy' law. Using suitable approximated problems, we prove existence of a solution and establish some properties.     

Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation

In this paper, a new one-dimensional space-fractional Boussinesq equation is proposed. Two novel numerical methods with a nonlocal operator (using nodal basis functions) for the space-fractional Boussinesq equation are derived. These methods are based on the finite volume and finite element methods, respectively. Finally, some numerical results using fractional Boussinesq equation with the maximally positive skewness and the maximally negative skewness are given to demonstrate the strong potential of these approaches. The novel simulation techniques provide excellent tools for practical problems. These new numerical models can be extended to two- and three-dimensional fractional space-fractional Boussinesq equations in future research where we plan to apply these new numerical models for simulating the tidal water table fluctuations in a coastal aquifer.