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1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
Advantages of the analytic element method for the solution of groundwater management problems 总被引：1，自引：0，他引：1
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
8.
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
9.
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
10.
Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking 
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下载免费PDF全文 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
11.
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
12.
Groundwater studies face computational limitations when providing local detail (such as well drawdown) within regional models. We adapt the Analytic Element Method (AEM) to extend separation of variable solutions for a rectangle to domains composed of multiple interconnected rectangular elements. Each rectangle contains a series solution that satisfies the governing equations and coefficients are adjusted to match boundary conditions at the edge of the domain and continuity conditions across adjacent rectangles. A complete mathematical implementation is presented including matrices to solve boundary and continuity conditions. This approach gathers the mathematical functions associated with head and velocity within a small set of functions for each rectangle, enabling fast computation of these variables. Benchmark studies verify that conservation of mass and energy conditions are accurately satisfied using a method of images solution, and also develop a solution for heterogeneous hydraulic conductivity with log normal distribution. A case study illustrates that the methods are capable of modeling local detail within a large-scale regional model of the High Plains Aquifer in the central USA and reports the numerical costs associated with increasing resolution, where use is made of GIS datasets for thousands of rectangular elements each with unique geologic and hydrologic properties, Methods are applicable to interconnected rectangular domains in other fields of study such as heat conduction, electrical conduction, and unsaturated groundwater flow. 相似文献
13.
对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差. 相似文献
14.
Parallel computing is a promising approach to alleviate the computational demand in conducting large-scale finite element analyses. This paper presents a numerical modeling approach for earthquake ground response and liquefaction using the parallel nonlinear finite element program, ParCYCLIC, designed for distributed-memory message-passing parallel computer systems. In ParCYCL1C, finite elements are employed within an incremental plasticity, coupled solid-fluid formulation. A constitutive model calibrated by physical tests represents the salient characteristics of sand liquefaction and associated accumulation of shear deformations. Key elements of the computational strategy employed in ParCYCL1C include the development of a parallel sparse direct solver, the deployment of an automatic domain decomposer, and the use of the Multilevel Nested Dissection algorithm for ordering of the finite element nodes. Simulation results of centrifuge test models using ParCYCLIC are presented. Performance results from grid models and geotechnical simulations show that ParCYCLIC is efficiently scalable to a large number of processors. 相似文献
15.
Time‐varying suspended sediment‐discharge rating curves to estimate climate impacts on fluvial sediment transport 下载免费PDF全文
下载免费PDF全文 This study presents time‐varying suspended sediment‐discharge rating curves to model suspended‐sediment concentrations (SSCs) under alternative climate scenarios. The proposed models account for hysteresis at multiple time scales, with particular attention given to systematic shifts in sediment transport following large floods (long‐term hysteresis). A series of nested formulations are tested to evaluate the elements embedded in the proposed models in a case study watershed that supplies drinking water to New York City. To maximize available data for model development, a dynamic regression model is used to estimate SSC based on denser records of turbidity, where the parameters of this regression are allowed to vary over time to account for potential changes in the turbidity‐SSC relationship. After validating the proposed rating curves, we compare simulations of SSC among a subset of models in a climate change impact assessment using an ensemble of flow simulations generated using a stochastic weather generator and hydrologic model. We also examine SSC estimates under synthetic floods generated using a peaks‐over‐threshold model. Our results indicate that estimates of extreme SSC under new climate and hydrologic scenarios can vary widely depending on the selected model and may be significantly underestimated if long‐term hysteresis is ignored when simulating impacts under sequences of large storm event. Based on the climate change scenarios explored here, average annual maximum SSC could increase by as much as 2.45 times over historical values. 相似文献
16.
The concept of polynomial‐fraction approximation is explored in this article to develop a nested type of systematic lumped‐parameter model for unbounded soil. Based on the optimal coefficients determined from the flexibility formulation, the reciprocal of the polynomial‐fraction is first taken to represent the dynamic stiffness function of foundation and then decomposed into a linear polynomial and another polynomial‐fraction. The nested division introduced in this study is operated to generate a nested form for this decomposed polynomial‐fraction, which directly corresponds to a nested discrete‐element model. The nested type of lumped‐parameter model is then easily constructed by connecting this nested discrete‐element model in series with another simple discrete‐element model corresponding to the linear polynomial. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
17.
Charles McLane 《Ground water》2024,62(1):150-156
A well-planned field data collection program should be designed to (1) collect a sufficient set of data of the right types at the right locations, and (2) collect a parsimonious set of data to avoid unnecessary costs. Combining PEST and a simple analytic element method (AEM) groundwater flow model for the site of interest provides a relatively simple, low-cost method of developing such a program. AEM models are well suited to this approach because they are quick to develop yet hydraulically accurate, reducing impacts on project budgets at early data collection planning stages; and quick to run, solving rapidly for the many iterations that PEST requires to generate good parameter estimates. This article shows two examples of this method: one for a steady state watershed model, and one for a transient pumping test project to demonstrate that PEST coupled with a simple AEM model that sketches out the key features of a site conceptual model can be an efficient tool in planning key parts of a hydrogeologic site investigation. 相似文献
18.
常规的三维时间域航空电磁模拟通常采用隐式步长方法进行时间离散,需要几次矩阵分解和上百次右端源项回带,计算效率较低.为了提高正演计算效率,本文提出使用有理Krylov方法求解时间域电场扩散方程.首先使用非结构四面体网格进行空间离散,采用Nédélec矢量基函数近似四面体单元内的电场;然后基于有限元离散给出矩阵指数和矢量乘积表示的电场显式解;最后采用有理Arnoldi算法构造Krylov子空间内的正交基函数并进一步求解矩阵指数与矢量的乘积,直接得到任意时刻的电场解向量,避免步长离散过程.此外,本文还提出一种指数加权偏移参数优化方法,使得有理Arnoldi近似在瞬变衰减晚期具备更高的精度,从而降低Krylov子空间阶数并提高计算效率.通过和层状模型解析解的对比验证了有理Krylov方法的精度.针对三维异常体模型使用全局网格和局部网格剖分并和其他数值方法比较,进一步说明了有理Krylov方法的有效性. 相似文献
19.
This paper presents a new statistical method for assimilating precipitation data from different sensors operating over a range of scales. The technique is based on a scale-recursive estimation algorithm which is computationally efficient and able to account for the nested spatial structure of precipitation fields. The version of the algorithm described here relies on a static multiplicative cascade model which relates rainrates at different scales. Bayesian estimation techniques are used to condition rainrate estimates on measurements. The conditioning process is carried out recursively in two sweeps: first from fine to coarse scales and then from coarse to fine scales. The complete estimation algorithm is similar to a fixed interval smoother although it processes data over scale rather than time. We use this algorithm to assimilate radar and satellite microwave data collected during the tropical ocean–global atmosphere coupled ocean–atmosphere response experiment (TOGA-COARE). The resulting rainrate estimates reproduce withheld radar measurements to within the level of accuracy predicted by the assimilation algorithm. 相似文献
20.
The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell’s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology. 相似文献