共查询到20条相似文献，搜索用时 31 毫秒
1.
A finite element procedure based on the extension of the saturated flow domain into the partially saturated zone above the free surface is proposed. The finite element equations are derived by using a pseudo variational principle which results into a residual or correction load vector. The steady or transient free surface is corrected by using the residual load in an iterative scheme. The proposed procedure uses only one (initial) mesh and does not require modification of the mesh during iterations. It is compared (qualitatively) with other procedures such as variable mesh and variational inequalities. The procedure provides satisfactory comparisons with a number of closed-form solutions and laboratory test results; two applications involving the latter are described in the paper. 相似文献
2.
A transient Green function due to suddenly applied line loads in an isotropic and homogeneous half-space is reported in this paper. The derivation of the half-space Green function in the Laplace and the Fourier transform spaces is first reviewed. Following an explicit inversion of the Fourier transform, the inverse Laplace transform is implemented along the contour integral on the p-complex plane in an integral form. The half-space Green function consists of full-space Green functions and a singularity-free complementary term. It can be easily incorporated into current transient boundary elements using the transient full-space Green function. Combined with finite elements, the half-space Green function can be used in a hybrid procedure to solve transient half-space problems without discretization of the free surface. Numerical results are presented to illustrate transient wave propagation in a half-space. 相似文献
3.
The method of conformal mapping is applied to the analysis of transient flow toward parallel periodic drains in a semi-infinite aquifer taking into consideration the non-linear boundary conditions on the free surface. The mapping function is expressed as a power series in time and the seepage domain is mapped onto a domain of an auxiliary complex variable. Mapping is performed in such a manner that the free surface will always remain the real axis. Calculations are carried out for different ratios of drain depth to drain spacing using various drain diameter to depth ratios. 相似文献
4.
An analytical solution for the space-time variation of contaminant concentration in one-dimensional transient groundwater flow in a homogenous semi-infinite aquifer, subjected to time-dependent source contamination, is derived. The uniform and time varying dispersion along transient groundwater flow is investigated under two conditions. First, the flow velocity distribution in the aquifer is considered as a sinusoidally varying function, and second, the flow velocity distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free, so the initial background concentration is considered as an exponentially decreasing function of the space variable which is tending to zero at infinity. It is assumed that dispersion is directly proportional to the square of the velocity, noting that experimental observations indicate that dispersion is directly proportional to the velocity with a power ranging from 1 to 2. The analytical solution is illustrated using an example and may help benchmark numerical codes and solutions. 相似文献
5.
The paper describes an optimization method for the solution of groundwater management problems. The method consists of a combination of the computation of horizontal plane groundwater flow with a free surface (finite element method) and a linear optimization procedure (simplex algorithm). Considering the special structure of data which result form computing the groundwater flow with the finite element method, and modifying the simplex algorithm, the solution of management problems with complex groundwater flow is realized without any difficulties. Compared to a flow computation alone the additional effort of the optimization (computer time and scope for data storage) is only small. 相似文献
6.
A unified approach to modeling flows of slightly compressible fluids through naturally fractured media is presented. The unified fractional differential model is derived by combining the flow at micro scale for matrix blocks and macro scale for fractures, using the transient interporosity flow behavior at the interface between matrix blocks and fractures. The derived model is able to unify existing transient interporosity flow models formulated for different shapes of matrix blocks in any medium dimensions. The model is formulated in the form of a fractional order partial differential equation that involves Caputo derivative of order 1/2 with respect to time. Explicit solutions for the unified model are derived for different axisymmetrical spatial domains using Hankel or Hankel–Weber finite or infinite transforms. Comparisons between the predictions of the unified model and those obtained from existing transient interporosity flow models for matrix blocks in the form of slabs, spheres and cylinders are presented. It is shown that the unified fractional derivative model leads to solutions that are very close to those of transient interporosity flow models for fracture-dominant and transitional fracture-to-matrix dominant flow regimes. An analysis of the results of the unified model reveals that the pressure varies linearly with the logarithm of time for different flow regimes, with half slope for the transitional fracture-to-matrix dominant flow regime vs. the fracture and matrix dominant flow regimes. In addition, a new re-scaling that involves the characteristic length in the form of matrix block volume to surface area ratio is derived for the transient interporosity flow models for matrix blocks of different shapes. It is shown that the re-scaled transient interporosity flow models are governed by two dimensionless parameters Θ and Λ compared to only one dimensionless parameter Θ for the unified model. It is shown that the solutions of the transient interporosity flow models for different shapes of matrix blocks are almost identical for the re-scaled variables. Furthermore, the driving parameters for solution behavior are identified based on asymptotic approximations for different flow regimes. It is found that the matrix diffusion and the matrix area-to-volume ratio affect the solution behavior only for the transitional fracture-to-matrix dominant flow regime, that the capacitance ratio affects the solution behavior only for transitional and matrix dominant flow regimes and that the fracture diffusion is involved in all three flow regimes. Similar identification of the driving parameters is also presented in the re-scaled case. 相似文献
7.
Arabinda Mukhopadhyay 《Pure and Applied Geophysics》1967,67(1):43-53
Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above. 相似文献
8.
Simon A. Mathias 《Ground water》2010,48(3):438-441
When seeking to predict plume geometry resulting from fluid injection through partially penetrating wells, it is common to assume a steady-state spherically diverging flow field. In reality, the flow field is transient. The steady-flow assumption is likely to cause overestimation of injection plume radius since the accommodation of fluid by increases in porosity and fluid density is ignored. In this paper, a transient solution is developed, resulting in a nonlinear ordinary differential equation expressing plume radius as a function of time. It is shown that the problem can be fully described by one type curve. A critical time, tc, is identified at which the percentage error of the steady-state flow solution compared to the fully dynamic problem is less than 1%. Only for large injection rates and low permeabilities, does tc become greater than 1 h. Nevertheless, an improved approximate solution is obtained by a simple linearization procedure. The critical time, tc for the new approximate solution is 0.3% of that required for the steady-state flow solution. 相似文献
9.
P.W. France 《Journal of Hydrology》1974,21(4):381-398
A numerical method is presented for analysing either steady state or transient three-dimensional groundwater flow problems. The governing equation is formulated in terms of the finite element process using the Galerkin approach, and cubic isoparametric elements are used to simulate the flow domain as these permit accurate modelling of curved boundaries. Particular attention is paid to the time dependent movement of the phreatic surface where an iterative technique based on the replacement of the original transient problem by a discrete number of steady state problems is used to effect a solution. Furthermore, in tracing the movement of the surface use is made of the element formulation theory in order to compute the normal to the boundary.The validity of the technique is first established by analysing a radially symmetrical problem for which an alternative analytical solution is available. Finally, a general three-dimensional flow system is studied for which there is no known analytical solution. It is shown that relatively few elements are required to yield practical solutions. 相似文献
10.
A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms
The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well. 相似文献
11.
On the solution of transient free-surface flow problems in porous media by the finite element method
A numerical procedure is presented to deal with solution of transient free-surface flows in porous media. The governing boundary-value problem for the piezometric potential is solved by the finite element method. The initial-value problem which describes the transient motion of the free-surface is solved by the method of quasi-linearization. The numerical scheme has been applied to isotropic and anisotropic earth dam problem and also to a ditch drainage problem. Excellent agreements have been reached when compared with known solutions. This computational procedure is shown to be stable and suitable for this class of problems with the aid of a digital computer. 相似文献
12.
Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks. 相似文献
13.
P.W. France 《Advances in water resources》1977,1(1):49-51
This paper describes an investigation into the motion of the water surface in a simple model surge tank, and the relevant factors governing its behaviour. The oscillation of the free water surface is an unsteady flow problem, which is amenable to a mathematical solution using a finite difference step-by-step integration procedure. For comparison, two such methods are presented: (i) a simple initial value method and (ii) a predictor-corrector technique. Computer programs have been developed linked to a graph plotter to give a visual presentation of the numerical solutions together with the experimental results of the damped oscillation of the water surface in the model surge tank. 相似文献
14.
A Laplace-transform analytic element method (LT-AEM) is described for the solution of transient flow problems in porous media. Following Laplace transformation of the original flow problem, the analytic element method (AEM) is used to solve the resultant time-independent modified Helmholtz equation, and the solution is inverted numerically back into the time domain. The solution is entirely general, retaining the mathematical elegance and computational efficiency of the AEM while being amenable to parallel computation. It is especially well suited for problems in which a solution is required at a limited number of points in space–time, and for problems involving materials with sharply contrasting hydraulic properties. We illustrate the LT-AEM on transient flow through a uniform confined aquifer with a circular inclusion of contrasting hydraulic conductivity and specific storage. Our results compare well with published analytical solutions in the special case of radial flow. 相似文献
15.
We consider common bank filtration systems and develop an explicit analytic solution representing steady, two-dimensional, groundwater flow to a horizontal well near a river in an unconfined aquifer. For the boundary-value problem investigated, we find that a unique solution exists for all negative well discharges. For positive discharges, a maximum value exists which corresponds to the formation of a cusp on the free surface. For positive discharges less than the maximum, the solution is not unique, consisting of two alternate configurations of the free surface. One solution includes a stable free surface on a single-valued physical plane, while the alternate solution includes a looped free surface lying on two sheets of a Riemann surface. Imposing a stability condition on the free surface results in a unique solution to the problem. We use the solution to investigate the behavior of the free surface under varying well discharges to identify stable pumping rates and predict well yield. In particular, we examine the well yield and the stability of the free surface when the head in the horizontal well is maintained at the top of the well screen. This condition is shown to produce a stable free surface for a wide range of well radii; the stability is independent of the hydraulic conductivity of the aquifer, the location of the well, or the presence of a skin resistance at the well. 相似文献
16.
Routing procedures have been used for determining the observed values of the dispersion coefficient in river mixing studies. In order to overcome the shortcomings of the existing routing procedures, we developed a new routing procedure capable of being applied under a transient concentration situation while accounting for river irregularities. The proposed routing procedure is based on the exact solution of the depth-averaged, two-dimensional, mass transport equation combined with the stream-tube concept and was verified through the tracer data acquired from field tests conducted in natural rivers located in Korea. The observed dispersion coefficients evaluated by the routing procedure exhibited a stream-wise variation along the rivers, in that a minimum value was seen in the straight region and a maximum value downstream of the apex of the bend. This variation was attributed to the flow dynamics of secondary currents induced by the meandering of the rivers. The dispersion coefficients obtained by the new method over the reach were in the same range of those calculated by other methods. 相似文献
17.
One of the great classical problems in theoretical seismology is Garvin’s problem, which deals with the response of an elastic half-space subjected to a blast line source applied in its interior. However, Garvin (Exact transient solution of the buried line source problem. Proceedings of the Royal Society of London, Series A 1956;528–541[4]) himself provided only the solution for points on the free surface of the half-space. Although a rigorous extension to points in the interior of the half-space was given nearly decade-and-a-half later by Alterman and Loewenthal (Algebraic expressions for the impulsive motion of an elastic half-space. Israel Journal of Technology 1969; 7 (6):495–504[1]), these scientists published their paper in a technical journal of rather restricted circulation, as a result of which their complete solution remained largely unnoticed by the geophysical and soil dynamics communities. This article revisits Garvin’s generalized problem, presents a concise rendition and summary together with a very effective and accurate simplification, and examines the response characteristics for a pair of buried source-receiver location. It also includes a compact and very effective Matlab program for its evaluation. 相似文献
18.
P. MAUERSBERGER 《水文科学杂志》2013,58(2):169-178
Abstract The aim of the present paper is to present some mathematical techniques for the solution of problems connected with three-dimensional steady-state groundwater flow with a free surface. The validity of Darcy's law is assumed. As no use is made of the Dupuit-Forschheimer approximation, the shape of the free surface and the velocity potential must be determined simultaneously from a non-linear boundary value problem. In order to demonstrate the use of a variational method and of error distribution principles for the solution of those problems by an example as simple as possible, we investigate the gravity flow of incompressible, homogeneous groundwater towards a circular well completely penetrating an isotropic, homogeneous, inelastic aquifer resting on a horizontal, impermeable substratum. 相似文献
19.
A numerical procedure is proposed to investigate the transient response of a group of rigid strip foundations resting on an elastic, homogeneous half-space subjected to either external forces or seismic motions. A fundamental solution is presented for uniform strip loadings with Heaviside function time-dependence applied on the half-space. In the procedure, each of the foundations is discretized into subelements. The tractions between the half-space and the subelements are assumed constant at every time step. The through-soil coupling effects between the foundations are studied numerically. 相似文献
20.
David E. Loper 《地球物理与天体物理流体动力学》2013,107(5):587-602
A benchmark test for flow in karstic aquifers is presented in the form of an exact solution of the harmonic variations of water flux and head within a karst conduit that is imbedded within a three-dimensional porous matrix having a free surface. The variations are driven by a prescribed variation of head applied at one end of the conduit. The benchmark consists of expressions for the spring discharge as a function of time and the conduit head and flux as functions of distance along the conduit and time. These expressions contain three dimensionless parameters, permitting development of a wide range of specific benchmark tests. The expressions are particularly simple in the case of an infinitely deep aquifer. This limiting solution should provide the most severe test for two-dimensional models of karst aquifer flow. Another limiting case of interest is that in which the conduit diameter is equal to the water depth. This limiting solution should provide the easiest test for two-dimensional models. 相似文献