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1.
The analytic element method (AEM) has been applied to a 15,000-km2 area of the Paleozoic carbonate rock terrain of Nevada. The focus is the Muddy River springs area, which receives 1.44 m3/s (51 ft3/s) of regionally derived ground water, and forms the Muddy River. The study was undertaken early in 2000 to support the development of a cooling water supply for a gas-fired generation facility 20 km south of the Muddy River springs. The primary objectives of the AEM modeling were to establish a better understanding of regional fluxes and boundary conditions and to provide a framework for examination of more local transient effects using MODFLOW. Geochemical evidence available in 2000 suggested two separate flow fields, one in the north discharging at the springs, and a southern area of small hydraulic gradients. To be conservative, however, hydraulic continuity between the two areas was maintained in the 2000 AEM model. Using new monitoring well data collected in the south, and analyses confirming that seasonal pumping effects in the north are not propagated to the south, a later AEM model that included a barrier calibrated with relative ease. The analytic element model was well suited for simulating an area larger than the immediate area of interest, was easy to modify as more information became available, and facilitated the stepwise development of multiple conceptual models of the site.  相似文献   

2.
In the simulation‐optimization approach, a coupled optimization and groundwater flow/transport model is used to solve groundwater management problems. The efficiency of the numerical method, which is used to simulate the groundwater flow, is one the major reason to obtain the best solution for a management problem. This study was carried out to examine the advantages of the analytic element method (AEM) in the simulation‐optimization approach, for the solution of groundwater management problems. For this study, the AEM and finite difference method (FDM) based flow models were developed and coupled with the particle swarm optimization (PSO)‐based optimization model. Furthermore, the AEM‐PSO and FDM‐PSO models developed were applied in hypothetical as well as real field conditions to address groundwater management problems and the results were compared. For the real field situation, the models developed were applied to the Dore River basin in France to minimize the installation and operational cost of new pumping wells taking the location and discharge of the pumping wells as decision variables. The constraints of the problem were identified with the help of stakeholders and water authority officials. The AEM flow model was developed to facilitate the management model particularly when at each iteration, the optimization model calls for a simulation model to calculate the values of groundwater heads. The results show that, at some points, the AEM‐PSO model is efficient in identifying the optimal location of wells and consequently results in optimal costs, sometimes difficult when using the FDM. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.  相似文献   

4.
We obtained an exact solution in terms of the discharge potential for a constant-strength line-sink that satisfies the modified Helmholtz equation for groundwater flow, for example for semi-confined flow and transient flow. The solution is obtained by integrating the potential for a point sink (well) along a straight line element. The potential for the point-sink is the modified Bessel function of the second kind and zero order K0. Since K0 cannot be integrated directly (in closed form) along a line-element, earlier solutions for a line-sink have been obtained by integrating polynomial approximations to K0. These approximations, however, are only valid up to a certain distance from the well and consequently impose a limit on the length of the line-sink. In this paper we integrate an exact series representation for K0 that is valid at any distance from the well, thus allowing integration along line-elements of any length, at least in theory. Numerical difficulties arise when evaluating our expressions at large distances from the line-sink, but these are shown to be of little consequence in practice. We made use of Wirtinger calculus to facilitate integration and also to allow us to arrive at exact expressions for the integrated flux over a poly-line and the total leakage over a domain. These properties are essential when using the solution in the context of the Analytic Element Method (AEM). We demonstrate our solution for the case of semi-confined flow (with leakage) and for the case of transient flow in the context of the Laplace Transform Analytic Element Method (LT-AEM).  相似文献   

5.
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   

6.
The two-dimensional implementation of the analytic element method (AEM) is commonly used to simulate steady-state saturated groundwater flow phenomena at regional and local scales. However, unlike alternative groundwater flow simulation methods, AEM results are not ordinarily used as the basis for simulation of reactive solute transport. The use of AEM-simulated flow fields is impeded by the discrepancy between a continuous representation of flow and a typically discrete representation of transport, and requires translation of the flow solution to a discrete analog. This paper presents a variety of methods for analytically calculating conservative discrete water fluxes and integrated components of the dispersion tensor across cell interfaces. An Eulerian finite difference method based on these AEM-derived parameters is implemented for use in simulation of 2D (vertically averaged) solute transport. This implementation is first benchmarked against existing methods that use standard finite difference flow solutions, then used to investigate the effects of an inaccurate discrete water balance. It is shown that improper translation of AEM fluxes leads to significant water balance errors and inaccurate simulation of contaminant transport.  相似文献   

7.
Analytic element ground water modeling as a research program (1980 to 2006)   总被引：2，自引：0，他引：2  
Kraemer SR 《Ground water》2007,45(4):402-408
Scientists and engineers who use the analytic element method (AEM) for solving problems of regional ground water flow may be considered a community, and this community can be studied from the perspective of history and philosophy of science. Applying the methods of the Hungarian philosopher of science Imre Lakatos (1922 to 1974), the AEM "research program" is distinguished by its hard core (theoretical basis), protective belt (auxiliary assumptions), and heuristic (problem solving machinery). AEM has emerged relatively recently in the scientific literature and has a relatively modest number of developers and practitioners compared to the more established finite-element and finite-difference methods. Nonetheless, there is evidence to support the assertion that the AEM research program remains in a progressive phase. The evidence includes an expanding publication record, a growing research strand following Professor Otto Strack's book Groundwater Mechanics (1989), the continued placement of AEM researchers in academia, and the further development of innovative analytical solutions and computational solvers/models.  相似文献   

8.
Fitts CR 《Ground water》2006,44(1):99-101
Although most current applications of the analytic element method are formulated for isotropic hydraulic conductivity, anisotropic domains can be modeled with analytic elements using the well-known coordinate transformation where one coordinate axis is scaled by the square root of the anisotropy ratio. If the standard analytic solution for steady radial flow to a well is used with this coordinate transformation, the resulting solution correctly models the far field but it does not meet the constant head boundary condition at the well radius. This could be a significant shortcoming if you are interested in the flow field close to the well or want to estimate the head at the pumping well. A new solution for two-dimensional steady flow to a well in an anisotropic domain is presented. This solution satisfies the governing equations exactly and meets the constant head boundary condition at the well radius exactly. It was derived using a conformal mapping.  相似文献   

9.
Strack OD 《Ground water》2006,44(1):91-98
We deal in this paper with an ongoing development of the analytic element method. We present in outline new analytic line elements that are suitable to model general flow fields, i.e., flow fields that possess a continuously varying areal inflow or outflow. These elements are constructed specifically to model the leakage through leaky layers that separate aquifers in leaky systems and to model transient effects. The leakage or release from storage underneath linear features is modeled precisely by the new elements; the singularity in leakage is matched exactly by the approximate solution. Applications are given for a problem involving leakage and for a case of transient flow. We note that the analytic elements can be used also to reproduce the effect of continuously varying aquifer properties, e.g., the hydraulic conductivity or the elevation of the base of the aquifer. In the latter case, the elements would reproduce the rotation of the flow field caused by the variation in properties, rather than the divergence as for the case of leakage.  相似文献   

10.
Plume containment using pump-and-treat (PAT) technology continues to be a popular remediation technique for sites with extensive groundwater contamination. As such, optimization of PAT systems, where cost is minimized subject to various remediation constraints, is the focus of an important and growing body of research. While previous pump-and-treat optimization (PATO) studies have used discretized (finite element or finite difference) flow models, the present study examines the use of analytic element method (AEM) flow models. In a series of numerical experiments, two PATO problems adapted from the literature are optimized using a multi-algorithmic optimization software package coupled with an AEM flow model. The experiments apply several different optimization algorithms and explore the use of various pump-and-treat cost and constraint formulations. The results demonstrate that AEM models can be used to optimize the number, locations and pumping rates of wells in a pump-and-treat containment system. Furthermore, the results illustrate that a total outflux constraint placed along the plume boundary can be used to enforce plume containment. Such constraints are shown to be efficient and reliable alternatives to conventional particle tracking and gradient control techniques. Finally, the particle swarm optimization (PSO) technique is identified as an effective algorithm for solving pump-and-treat optimization problems. A parallel version of the PSO algorithm is shown to have linear speedup, suggesting that the algorithm is suitable for application to problems that are computationally demanding and involve large numbers of wells.  相似文献   

11.
This paper introduces a new method for simulating large-scale subsurface contaminant transport that combines an Analytic Element Method (AEM) groundwater flow solution with a split-operator Streamline Method for modeling reactive transport. The key feature of the method is the manner in which the vertically integrated AEM flow solution is used to construct three-dimensional particle tracks that define the geometry of the Streamline Method. The inherently parallel nature of the algorithm supports the development of reactive transport models for spatial domains much larger than current grid-based methods. The applicability of the new approach is verified for cases with negligible transverse dispersion through comparisons to analytic solutions and existing numerical solutions, and parallel performance is demonstrated through a realistic test problem based on the regional-scale transport of agricultural contaminants from spatially distributed sources.  相似文献   

12.
The Analytic Element Method (AEM) provides a convenient tool for groundwater flow analysis in unbounded continuous domains. The AEM is based on the superposition of analytic functions, known as elements, useful at both regional and local scales. In this study, analytic elements for strip aquifers are presented. Such aquifers occur in riverine or coastal deposits and in outcrop zones of confined aquifers. Local flow field is modelled indirectly, using a reference plane related to the aquifer domain through the Schwarz‐Christoffel transform. The regional flow is obtained as a solution of the one‐dimensional flow equation. The proposed methodology was tested by modelling two hypothetical situations, which were compared to exact solutions. It is shown that regional boundaries can be reproduced exactly while local fields are adequately reproduced with analytic elements. The developed elements are applied to simulate a real flow field in northeastern Brazil showing good agreement with measured water levels. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

13.
A new approach is presented for improving the computational efficiency of regional-scale ground water models based on the analytic element method (AEM). The algorithm is an extension of the existing "superblock" algorithm, which combines the effects of multiple analytic elements into Laurent series and Taylor series (superblock expansions). With the new "nested superblock" formulation, Laurent series are nested in a hierarchical (quad-tree) data structure with direct mathematical relationships between parent and child superblock coefficients. Nested superblocks significantly accelerate the evaluation of the complex potential and discharge function in models that contain a large number of analytic elements at multiple scales. This evaluation process, the primary computational cost of AEM models, is required to determine the element coefficients, generate contour plots, and trace pathlines. The performance of the nested superblocks is demonstrated with a simplified model based on the Lake Ontario watershed geometry comprising thousands of hydrogeologic features at multiple geographic scales.  相似文献   

14.
Comprehensive studies of water resources systems require integration of modeling tools and data associated with individual processes. An object-oriented approach is presented here that associates ground water models based upon the analytic element method (AEM) with geographic information system (GIS) geodatabase features using an AEM Model Interface. Each aquifer object contains a prescribed geometry, a mathematical representation in the AEM, and GIS hydrogeologic data. The synergistic understanding inherent in such an approach is illustrated by a study linking local AEM model predictions of water elevation with ground water geodatabase objects. This AEM Model Interface provides a key component in establishing a common object-oriented geodatabase modeling approach linking ground water to a variety of natural and social processes.  相似文献   

15.
The analytic element method is well suited for the Gardner hydraulic conductivity function, but is limited in describing real soils. Therefore, parameter equivalence between the van Genuchten and Gardner hydraulic conductivity functions is explored for the case of steady vertical flow through a homogeneous medium with a single inclusion, i.e., a binary soil. The inclusion has different hydraulic parameters than the background medium. Equivalence is established using three methods: (1) effective capillary drive; (2) capillary length; (3) and a least-squares optimization method that aims to fit a Gardner function to a corresponding van Genuchten function by minimizing the difference in log conductivity over a specified pressure range. Comparisons between hydraulic models are made based on scatterplots of pressure head and the vertical Darcian flux obtained using a finite-element numerical solution with both constitutive relations. For applicability of an equivalent Gardner function over a broad range of pressure heads, the crossover pressure must be maintained between the two parametric functions. The crossover pressure is defined as the pressure in which the hydraulic conductivity of the inclusion is equal to the background. It can be shown that a hybrid methodology of preserving the crossover pressure exactly and using the effective capillary drive will result in hydraulic parameters that are easily obtained and provide good agreement between the conductivity functions of the GR model to the VG model.  相似文献   

16.
Multilayer analytic element modeling of radial collector wells   总被引：1，自引：0，他引：1  
A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms.  相似文献   

17.
Writing Analytic Element Programs in Python   总被引：1，自引：0，他引：1  
The analytic element method is a mesh-free approach for modeling ground water flow at both the local and the regional scale. With the advent of the Python object-oriented programming language, it has become relatively easy to write analytic element programs. In this article, an introduction is given of the basic principles of the analytic element method and of the Python programming language. A simple, yet flexible, object-oriented design is presented for analytic element codes using multiple inheritance. New types of analytic elements may be added without the need for any changes in the existing part of the code. The presented code may be used to model flow to wells (with either a specified discharge or drawdown) and streams (with a specified head). The code may be extended by any hydrogeologist with a healthy appetite for writing computer code to solve more complicated ground water flow problems.  相似文献   

18.
An analytic approach is presented for the simulation of variations in the groundwater level due to temporal variations of recharge in surficial aquifers. Such variations, called groundwater dynamics, are computed through convolution of the response function due to an impulse of recharge with a measured time series of recharge. It is proposed to approximate the impulse response function with an exponential function of time which has two parameters that are functions of space only. These parameters are computed by setting the zeroth and first temporal moments of the approximate impulse response function equal to the corresponding moments of the true impulse response function. The zeroth and first moments are modeled with the analytic element method. The zeroth moment may be modeled with existing analytic elements, while new analytic elements are derived for the modeling of the first moment. Moment matching may be applied in the same fashion with other approximate impulse response functions. It is shown that the proposed approach gives accurate results for a circular island through comparison with an exact solution; both a step recharge function and a measured series of 10 years of recharge were used. The presented approach is specifically useful for modeling groundwater dynamics in aquifers with shallow groundwater tables as is demonstrated in a practical application. The analytic element method is a gridless method that allows for the precise placement of ditches and streams that regulate groundwater levels in such aquifers; heads may be computed analytically at any point and at any time. The presented approach may be extended to simulate the effect of other transient stresses (such as fluctuating surface water levels or pumping rates), and to simulate transient effects in multi-aquifer systems.  相似文献   

19.
A three-dimensional procedure based on the finite element method is proposed for transient free surface seepage. It involves solution of the governing equations by using a time integration scheme. The procedure is applied for solution of confined, and transient free surface flow; the latter includes verification with respect to test results from a laboratory model. It is also applied to free surface flow through a dam with a crack.  相似文献   

20.
The Beerkan method based on in situ single‐ring water infiltration experiments along with the relevant specific Beerkan estimation of soil transfer parameters (BEST) algorithm is attractive for simple soil hydraulic characterization. However, the BEST algorithm may lead to erroneous or null values for the saturated hydraulic conductivity and sorptivity especially when there are only few infiltration data points under the transient flow state, either for sandy soil or soils in wet conditions. This study developed an alternative algorithm for analysis of the Beerkan infiltration experiment referred to as BEST‐generalized likelihood uncertainty estimation (GLUE). The proposed method estimates the scale parameters of van Genuchten water retention and Brooks–Corey hydraulic conductivity functions through the GLUE methodology. The GLUE method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the goodness‐of‐fit between modelled and observed data. The results showed that using a combination of three different likelihood measurements based on observed transient flow, steady‐state flow and experimental steady‐state infiltration rate made the BEST‐GLUE procedure capable of performing an efficient inverse analysis of Beerkan infiltration experiments. Therefore, it is more applicable for a wider range of soils with contrasting texture, structure, and initial and saturated water content. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

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