多重点源自由面波运动规律数值模拟

基于带耗散源格林函数去奇异积分数值方法,建立了均匀流浸没下双点源自由面波高计算模型,研究在不同耗散系数、弗劳德数及不同点源距离下自由面波高的变化规律以及自由面波形等高线的变化规律.数值模拟结果与前人的数值结果作验证比对,吻合较好.     

自由面重力流的边界积分方程——反演法

本文对求解自由面重力流提出了一种新的数值方法.在利用Мусхелишвилн.Н,И.学派数学理论的基础上,再通过变换,我们得到了物理平面上的非奇异边界积分方程,从而克服了用解析函数理论研究该类问题时,固壁边界未知待求的困难,为利用解析函数理论研究自由面重力流开辟了新的广阔途径.理论研究和计算表明,本文方法收敛性好、收敛速度快、运算量小,与现有方法相比有明显的优越性.文中计算了挑射水流和闸孔出流,计算结果与实验吻合.     

半浮区液桥中热毛细对流的自由面振荡

本文研究了半浮区小液桥中热毛细振荡对流的自由面变形.用实验的方法给出了自由面振荡的相对位移和相对位相差,给出了不同外加温差时自由面振荡的特性.本文结果还揭示了一类表面波,这种波动具有小扰动的特征,并在液桥的一个角区具有反常大的振幅.     

一个新的有自由面渗流问题的变分不等式提法

建立了一个新的有自由面渗流问题的变分不等式提法,提法通过将潜在出渗面上的边界条件提为Signorini型条件,从而从理论上消除了出渗点的奇性并解决了出渗点的定位问题．与其它变分不等式提法相比,该提法有更好的数值稳定性．     

水箱突然起动的水动压力问题

在本文中,应用Lagrange方法讨论水箱突然起动的水动压力问题.求得了自由面形状和作用在水箱壁上的动态压力系数.也证实了在自由面附近,压力系数的奇性仅是对数奇性.     

基于遗传算法的岩体参数辨识研究

目前,对于岩体流固耦合分析研究已经很多,而耦合分析常常受困于计算参数的取值,因此对两场耦合模型中的计算参数反演分析是非常必要的.根据实测的水头、位移资料,利用遗传算法,建立了等效连续岩体渗流场与应力场耦合计算参数辨识模型.并对某算例在库水位下降情况下,以渗流场与应力场耦合正分析计算结果作为"实测值",进行两场耦合参数辨识分析.从参数辨识的结果来看,验证了所提出的思路、方法以及程序的正确性和可行性.两场耦合计算参数进行反演分.析,对于两场耦合模型的建立和计算结果的可靠性是非常有意义的.     

煤层瓦斯流动的数学模型及其理论分析

本文来自煤矿生产实际,研究钻孔瓦斯的压力分布及涌出规律,其数学模型是非线性渗流方程。 文章包括四部份:1.用渗流理论导出微分方程;2.线性化方程韭用分离变量法解之;3.涌出量的计算;4.解的收敛性。     

径向低渗非Darcy渗流动边界半解析模型

低渗油藏渗流过程中普遍存在启动压力梯度(TPG).考虑低渗渗流特征,建立了平面径向低渗非Darcy渗流动边界数学模型,给出了计算动边界移动速度的公式,通过Laplace变换结合无穷级数方法求得了模型的半解析解,并进行了Stehfest数值反演.详细讨论与分析了动边界问题特性、动边界变化和传播情况,解释了启动压力梯度导致动边界不断向外扩展的现象.计算了启动压力梯度对井底压力、压力导数的影响,并给出不同条件下的地层压力分布曲线和Gringarten-Bourdet图版,同时给出了实例分析.研究发现:低渗渗流模型与常规渗流模型有着显著不同,低渗非Darcy渗流压力降是随时间扩展的,在动边界外的地层压力降为零,压力分布曲线呈现紧支性.针对具有动边界的低渗透问题,需充分考虑启动压力梯度与动边界的影响,该模型为低渗油藏渗流机理和开采动态、解释与数值模拟提供了一定的理论基础.     

半浮区液桥振荡对流的自由面振荡

将正交光栅(20L/mm)投影在小尺度液桥表面,接受其反射的正交光栅畸变象,可反演计算出液桥自由面形状.根据这一原理,我们测量了小浮区液桥面形及其振荡的二维形变过程.该实验结果进一部揭示了热毛细振荡对流的机理,特别是自由面的三维变化特征,同时,也为空间实验完成了实验室的原理研究.     

关于混凝土坝基渗流系统最优线态控制计算的惩罚移位法

研究了惩罚移位法应用于混凝土坝基渗流系统最优控制的计算 ,构造了其逼近程序 ,并证明了这种方法在适当的 Hilbert空间的收敛性 .     

Approximate solution methods in mechanics analysis of a class of nonlinear seepage problems by a finite-element method

We analyze the nonlinear boundary-value problem of seepage under a subsurface hydrotechnical construction over an inclined rectilinear aquifer. The method of inverse boundary-value problems is applied, using the velocity hodograph plane in which the original problem is reduced to a linear problem. The linear problem is solved in the general case using the finite-element method. A computer program realizing the proposed algorithms has been developed. We have used this program to run a series of numerical experiments, reaching certain conclusions about the behavior of the main seepage characteristics.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 75–80, 1985.     

Simulation of seepage flows from channels

Plane steady-state seepage in a homogeneous isotropic ground from channels through a layer of soil with an underlying highly permeable pressurized water-bearing layer when the ground possesses capillarity and there is evaporation from the free surface is considered in a hydrodynamic formulation. To investigate it, a mixed multiparametric boundary-value problem of the theory of analytical functions is formulated, which is solved using the Polubarinova-Kochina method and conformal mapping of the regions of a special form, typical of problems of underground hydromechanics. On the basis of this model, an algorithm for calculating the capillary spreading of water and seepage flow is developed in situations when the ground capillarity is taken into account in the seepage of water from channels, as well as evaporation from the free surface of the ground waters, and also backwater of the underlying highly permeable stratum. Using the exact analytical relations obtained and numerical calculations, a hydrodynamic analysis of the structure and characteristic features of the simulated process, and also of the effect of all the physical parameters of the system on the seepage characteristics, is carried out. Limit and special cases, related to the absence of one or two of the three factors, characterizing the simulated process are considered: the ground capillarity, evaporation from the free surface, and also backwater of the underlying highly permeable water-bearing layer. The results of the calculations are compared with similar seepage characteristics with a similar scheme, but in which the flow region is underlaid by an impenetrable base.     

Investigation of the effect of seepage or evaporation from a free surface by the method of circular polygons

It is proposed to use a technique developed for polygons in polar nets to integrate equations of the Fuchs class that arise when solving a wide range of problems of plane steady seepage flow using the Polubarinova-Kochina method, based on the use of the analytical theory of linear differential equations. It is shown that, for a large class of pentagons in domains where the flows,which are very characteristic of seepage problems when there is infiltration or evaporation from the free surface, have a complex velocity, the solution of the problem of determining the unknown parameters which appear in the conformal mapping can be completed. In this case, the mapping is carried out in closed form in terms of elementary functions and it is simple and convenient for subsequent application. The results obtained are used to solve the problem of seepage from a channel, taking account of the capillarity of the ground when there is evaporation from the free surface. The results of numerical calculations are presented and a hydrodynamic analysis of the effect of the basic physical parameters of the model on the dimensions of the saturation zone is given.     

非稳态渗流的自由边界问题

随着经济建设的高速发展,各种地下工程大量增加,如水坝和高层建筑的基础、地铁和隧道、水井和油井等。那里,介质中的渗流现象往往是工程单位需要考虑的重要问题。佘颖禾等在《应用数学和力学》第17卷6期中曾经给出了具有自由边界的稳态渗流的变分不等式模式及有限元解。本文中,以抽水井为例,进一步研究了非稳态渗流问题的变分不等式模式及其有限元解法。结果表明,对于非稳态的渗流问题,这种方法同样能避免传统的自由边界的迭代过程,为简单而快速地进行数值分析提供方便。     

Singular integral equations applied to free surface seepage from non-linear channels

The problem of two-dimensional seepage from a non-linear channel through a homogeneous medium underlain at a finite depth by a drain will be considered. A new approach is given, transforming the seepage problem to a non-linear singular integral equation for which the unique existence of the solution is proved. The free boundaries of the seepage region can be described explicitly.     

A variational inequality formulation for unconfined seepage problems in porous media

In the existing variational inequality formulations for the unconfined seepage problem in porous media, the seepage point, namely the exit point of the free surface, is a singular point and how to locate the seepage point exactly has been an open issue. By generalizing Darcy’s law applied solely to the saturated zone in an earth dam to the entire dam including the no-flow zone, a new variational inequality formulation is presented. The new formulation imposes a boundary condition of Signorini’s type on the potential seepage boundary and the seepage point turns out to be such a point that makes both inequalities in Signorini’s complementary condition become equalities. Singularity of the seepage point is accordingly eliminated. A strategy is developed for overcoming the mesh-dependency in the finite element implementation.     

Unsteady seepage analysis using local radial basis function-based differential quadrature method

Numerical simulation of two-dimensional transient seepage is developed using radial basis function-based differential quadrature method (RBF-DQ). To the best of the authors’ knowledge, this is the first application of this method to seepage analysis. For the general case of irregular geometry and unstructured node distribution, the local form of RBF-DQ was used. The multiquadric type of radial basis functions was selected for the computations, and the results were compared with analytical, finite element method, and existing numerical solutions from the literature. Results of this study show that localized RBF-DQ can produce accurate results for the analysis of seepage. The method is meshfree and easy to program, but as with previous applications of RBFs, requires careful selection of suitable shape parameters. A practical method for estimating suitable shape parameters is discussed. For time integration, Crank–Nicolson, Galerkin and finite difference methods were applied, leading to stable results.     

Three-dimensional non-Darcy flow analysis using a hybrid numerical model

A hybrid numerical model is developed for the simulation of three-dimensional, unsteady non-Darcy flow through an unconfined aquifer. The major problem in analysing flow through unconfined aquifers is that they involve two boundaries, namely a surface of seepage and a free surface, the location of which is not known beforehand. The model that is presented here determines these boundaries via a two stage modelling technique. In the first stage a one-dimensional finite difference model is used to estimate the surface of seepage height whereas in the second stage a vertically integrated finite element model determines the free surface solution within the flow domain. A comparison between numerical and experimental results is included which indicates the sensitivity of the numerical solution to the selected aquifer parameters, particularly to those associated with the determination of the height of the surface of seepage.     

On the use of equations of the Fuchs class to calculate seepage from channels and irrigation ditches

Several schemes for seepage flows from the channels and ditches of irrigation systems through a layer of soil underlaid by a highly permeable artesian water-bearing table or an impermeable foundation are considered within the framework of the theory of the plane steady seepage of an incompressible liquid oblying to Darcy's law. Mixed multiparameter boundary value problems of the theory of analytic functions are formulated for their investigation, which are solved using Polubarinova–Kochina's method and integration of differential equations of the Fuchs class that are characteristic in problems of subterranean hydromechanics. On the basis of these models, algorithms are developed for calculating the dimensions of the saturation zone in cases when, in the seepage of water from channels and irrigation ditches, there is a need to estimate the combined effect on the pattern of motion of such important factors as the backwater from the underlying artesian water table or confining bed, the soil capillarity and the evaporation of ground waters from the free surface. The results of the calculations for all the flow schemes are compared for identical seepage characteristics.