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About 2,536 papers for “Analytic element method”

Hydrogeological Uncertainty Estimation with the Analytic Element Method

Maximilian Ramgraber, Mario Schirmer · 2020

Earth and Space Science Open Archive This preprint has been submitted to and is under consideration at Water Resources Research. ESSOAr is a venue for early communication or feedback before peer review. Data may be preliminary.Learn more about preprints preprintOpen AccessYou are viewing the latest version by default [v1]Hydrogeological Uncertainty Estimation with the Analytic Element MethodAuthorsMaximilianRamgraberiDMarioSchirmeriDSee all authors Maximilian RamgraberiDCorresponding Author• Submitting AuthorEawag - Swiss Federal Institute of Aquatic Science and TechnologyiDhttps://orcid.org/0000-0003-3508-6214view email addressThe email was not providedcopy email addressMario SchirmeriDEAWAGiDhttps://orcid.org/0000-0002-0714-2525view email addressThe email was not providedcopy email address

Cited by 0

Hydrogeological Uncertainty Estimation With the Analytic Element Method

Maximilian Ramgraber, Mario Schirmer · Water Resources Research · 2021

Abstract Uncertainty estimation plays an important part in practical hydrogeology. With most of the subsurface unobservable, attempts at system characterization will invariably be incomplete. Uncertainty estimation, then, must quantify the influence of unknown parameters, forcings, and structural deficiencies. In this endeavor, numerical modeling frameworks can resolve a high degree of subsurface complexity and its associated uncertainty. Where boundary uncertainty is concerned, however, numerical frameworks can be restrictive. The interdependence of grid discretization and its enclosing boundaries render exploration of uncertainties in their extent or nature challenging. The analytic element method (AEM) may be an interesting complement, as it is computationally efficient, economic with its parameter count, and does not require enclosure through finite boundaries. These properties make AEM well suited for uncertainty estimation, particularly in data‐scarce settings or exploratory studies. In this study, we explore the use of AEM for flow field uncertainty estimation, with a particular focus on boundary uncertainty. To induce diverse, uncertain regional flow more easily, we propose a new element based on a Möbius transformation. We include this element in a simple Python‐based AEM toolbox and benchmark it against MODFLOW. Coupling AEM with a Markov Chain Monte Carlo routine using adaptive proposals, we explore its use in a synthetic case study. We find that AEM permits efficient uncertainty estimation for groundwater flow fields, which may form a basis for stochastic Lagrangian transport modeling or can support advanced model design by informing the placement of numerical model boundaries.

Cited by 0Open access

Elonged aquifer flow modeling based on analytic element method

Batista, Jose Anderson do Nascimento, 1977- · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2006

O método de elementos analíticos tem se mostrado uma alternativa conveniente para a construção de modelos regionais de escoamento subterrâneo. O método utiliza soluções elementares analíticas e, portanto, não necessitam de contornos artificiais. Entretanto, a caracterização de fronteiras externas de aqüíferos considerados longos (aqüíferos longos) acarreta dúvidas quanto à presença do efeito de borda na simulação. Assim, neste trabalho, o método de elementos analíticos é estendido para a modelagem de escoamentos em aqüíferos longos eliminando-se a possibilidade da presença de efeitos de borda. O domínio desses aqüíferos é mapeado em um semi-plano utilizando-se a transformação de Schwarz-Christoffel. Dessa forma, elementos de regime estacionário são mapeados juntamente com o domínio para o semi-plano e, portanto, sua formulação é modificada. Os contornos do semi-plano, por sua vez, são representados pelo método de imagens. Elementos de escoamento transiente são abordados utilizando-se a formulação de Zaadnoordijk. São realizadas correções algébricas e computacionais na formulação desses elementos. No entanto, o mapeamento de domínio não é extensivo aos elementos transientes. Sua aplicação em aqüíferos longos é feita de maneira aproximada utilizando-se apenas o método de imagens diretamente sobre o aqüífero. Em seguida, a extensão proposta para o método de elementos analíticos é analisada em um problema hipotético. Finalmente, é feita uma modelagem para a avaliação de impactos ambientais devidos a um sistema de captação de água localizado em uma porção do aqüífero Barreiras no Estado do Rio Grande do Norte sobre a Lagoa do Bonfim. O modelo é calibrado em regime permanente fornecendo uma estimativa de recarga de 24 mm/mês e, então, estima os impactos permanentes do sistema sobre a Lagoa do Bonfim, onde é feita a captação. O impacto do bombeamento reduz aproximadamente 5,36 m do nível de água natural da lagoa. Um cenário de seca é, também, simulado em regime transiente. A partir dos resultados obtidos avalia-se que dois meses de ausência de recarga direta aumentam aproximadamente 0,5 m a redução do nível de água da Lagoa do Bonfim

Cited by 0

Simulation of groundwater flow by the analytic element method

Sardar Muhammad Hussain · 2017

Edson Cezar Wendland, without their constant help, deep interest, kind and attentive guidance, the completion of this thesis was not possible. I appreciate all their contributions of time, ideas, accommodative attitude, thought provoking guidance, immense intellectual input, patience and sympathetic behavior. I want to extend my

Cited by 8Open access

Ground Water Modeling Applications Using the Analytic Element Method

Randall J. Hunt · Ground Water · 2006

Though powerful and easy to use, applications of the analytic element method are not as widespread as finite-difference or finite-element models due in part to their relative youth. Although reviews that focus primarily on the mathematical development of the method have appeared in the literature, a systematic review of applications of the method is not available. An overview of the general types of applications of analytic elements in ground water modeling is provided in this paper. While not fully encompassing, the applications described here cover areas where the method has been historically applied (regional, two-dimensional steady-state models, analyses of ground water-surface water interaction, quick analyses and screening models, wellhead protection studies) as well as more recent applications (grid sensitivity analyses, estimating effective conductivity and dispersion in highly heterogeneous systems). The review of applications also illustrates areas where more method development is needed (three-dimensional and transient simulations).

Cited by 53Open access

Simulation of groundwater flow by the analytic element method

Sardar Muhammad Hussain · Americanae (AECID Library) · 2017

Groundwater studies face computational limitations when providing local detail within regional models. The researchers are concentrated on applying the numerical models to minimize the difference between the physical reality and the implemented numerical model by considering the minimum computational cost. This work consists of the study of line-elements (such as line-doublets, circles, polygons, fractures) using the Analytic Element Method (AEM) for groundwater flow. In this work, we consider the study of two-dimensional groundwater flow in fractured porous media by the Analytic Element Method. We develop a numerical solution based on a series expansion for a problem with more than one fracture. Each fracture has an influence that can be expanded in a series that satisfies Laplaces equation exactly. In the series expansion, the unknown coefficients are obtained from the discharge potentials of all other elements that are related to the expansion coefficients. Sizes, locations and conductivities for all inhomogeneities are selected arbitrarily. This work also discusses a matrix method obtained by imposing the intern boundary conditions for the Analytic Element Method. The convergence analysis of a Gauss-Seidel type iterative method is also discussed.

Cited by 0Open access

Model Calibration Techniques for Use with the Analytic Element Method

Barry F. Power, Randal J. Barnes · Ground Water · 1993

Abstract The combination of the analytic element method and a nonlinear parameter estimation technique forges a computationally efficient, information‐rich, and cost‐effective solution to the inverse ground‐water flow problem. The recommended model calibration method uses a nonlinear least‐squares objective, as quantified by misfitting the measured and modeled heads, and a modified Levenberg‐Marquardt algorithm. As detailed and demonstrated by a steady‐state regional aquifer model of Bemidji, Minnesota, automated calibration techniques make ground‐water modeling feasible for a wider variety of projects where tight budgets and a lack of tools may have previously made such modeling inappropriate.

Cited by 5

Laplace Transform Analytic Element Method for Transient Groundwater Flow Simulation

Kristopher Kuhlman · UA Campus Repository (The University of Arizona) · 2008

The Laplace transform analytic element method (LT-AEM), applies the traditionally steady-state analytic element method (AEM) to the Laplace-transformed diffusion equation (Furman and Neuman, 2003). This strategy preserves the accuracy and elegance of the AEM while extending the method to transient phenomena. The approach taken here utilizes eigenfunction expansion to derive analytic solutions to the modified Helmholtz equation, then back-transforms the LT-AEM results with a numerical inverse Laplace transform algorithm. The two-dimensional elements derived here include the point, circle, line segment, ellipse, and infinite line, corresponding to polar, elliptical and Cartesian coordinates. Each element is derived for the simplest useful case, an impulse response due to a confined, transient, single-aquifer source. The extension of these elements to include effects due to leaky, unconfined, multi-aquifer, wellbore storage, and inertia is shown for a few simple elements (point and line), with ready extension to other elements. General temporal behavior is achieved using convolution between these impulse and general time functions; convolution allows the spatial and temporal components of an element to be handled independently.Comparisons are made between inverse Laplace transform algorithms; the accelerated Fourier series approach of de Hoog et al. (1982) is found to be the most appropriate for LT-AEM applications. An application and synthetic examples are shown for several illustrative forward and parameter estimation simulations to illustrate LT-AEM capabilities. Extension of LT-AEM to three-dimensional flow and non-linear infiltration are discussed.

Cited by 7

An Analytic Element Method solution for multispecies reactive contaminant transport

Anton Köhler, James R. Craig, Prabhas Kumar Yadav et al. · 2025

A new analytic element approach is presented for steady-state reactive contaminant transport modelling with circular boundaries. Two solute compounds (electron donor and electron acceptor) are assumed to undergo an instantaneous and binary reaction [1] in a uniform flow field, forming a steady plume [2]. Transformations of the advection-dispersion-reaction equation are applied resulting in a reactive contaminant transport system governed by the modified Helmholtz equation. Comprehensive solutions to a single as well as multiple superimposed, interacting circular contaminant (electron donor) source elements are expressed by infinite series expansions of Mathieu functions [3]. The concentration of the electron donor and electron acceptor can be calculated at any point in the domain, while boundary conditions are met approximately, by adjusting the unknown coefficients of the truncated series of Mathieu functions.  Accuracy at the boundary interfaces is increased with an increase of number of terms used in the Mathieu functions series expansion. The potential of this novel approach lies in the flexibility of boundary conditions, while maintaining computational efficiency.The model is implemented using the Python programming language. Model verification was achieved by evaluating the residual of a central difference scheme, evaluation of the error along the boundary interfaces and a comparison with a simple MODFLOW / MT3DMS model setup. Current development includes expansion of the model to line source elements and discontinuous contaminant sources. Further advancements may be achieved by increasing source shape complexity of contaminant sources by superimposing a large number of elements and introducing remediation actions in the form of interacting electron acceptor elements.[1]           O. A. Cirpka, Å. Olsson, Q. Ju, Md. A. Rahman, and P. Grathwohl, ‘Determination of Transverse Dispersion Coefficients from Reactive Plume Lengths’, Groundwater, vol. 44, no. 2, pp. 212–221, 2006, doi: 10.1111/j.1745-6584.2005.00124.x.[2]           R. Liedl, A. J. Valocchi, P. Dietrich, and P. Grathwohl, ‘Finiteness of steady state plumes’, Water Resources Research, vol. 41, Dec. 2005, doi: 10.1029/2005WR004000.[3]           M. Bakker, ‘Modeling groundwater flow to elliptical lakes and through multi-aquifer elliptical inhomogeneities’, Advances in Water Resources, vol. 27, no. 5, pp. 497–506, May 2004, doi: 10.1016/j.advwatres.2004.02.015.

Cited by 0Open access

Novel hydrogeologic characterization methods: utilizing the analytic element method in hydrogeophysical studies

Koehn, Weston · K-State Research Exchange (Kansas State University) · 2020

An accurate conceptualization of groundwater-surface water connectivity is critical for quantification of fluxes between rivers and aquifers. Point based hydrologic data provides a useful indicator to delineate an aquifers response to changes in streamflow; however, supplementary hydrogeologic information is often needed to fully constrain connectivity patterns due to the presence of focused recharge pathways. Electrical resistivity tomography (ERT) is a near surface geophysical method that determines the electrical resistivity distribution within the earth. Electrical resistivity is an intrinsic material property that is strongly correlated to hydrogeologic properties (e.g., water content, porosity, pore fluid salinity, clay content). The spatial and temporal distribution of electrical resistivity provides insight into the hydrologic state of sediments. Ultimately, changes in electrical resistivity across space and time provide of level of understanding about hydrogeologic processes that is unmatched by the analysis of point based hydrologic measurements alone. ERT surveys were conducted along the Arkansas River in Western Kansas to depict the hydrologic state of riverbed sediments, and to gain insight on the hydrologic response of the sediments across changes in streamflow and the hydrogeologic landscape. The electrical resistivity profiles revealed large contrasts in resistivity beneath portions of the inundated riverbed, indicating different regimes of groundwater-surface water (gw-sw) connectivity persist both spatially and temporally. Although the initial results of the study indicated that ERT can be used to observe differences in gw-sw connectivity through time and space, a more rigorous hydrogeologic interpretation of ERT surveys is needed to bridge the gap between quantitative groundwater models and the information provided by geophysical earth models. This motivated the inclusion of the Analytic Element Method (AEM) into geophysical inversion and ERT survey design to further advance the ability of near surface geophysics to fully exploit the hydrogeologic information inherent geophysical data. Electrical conduction through soil was modelled using the AEM. Soil was represented using interconnected rectangular elements, each with a constant electrical resistivity. The forward response of an ERT array was generated over layered resistivity models. The AEM model matched electrostatic boundary an interface conditions to high accuracy for lowly and highly resistivity layers, as well as for isolated inclusions within uniform backgrounds. The implementation of a particle swarm optimization scheme was used to reconstruct resistivity models from synthetic data, which were in good agreement with the known model within the theoretical depths investigation of the simulated array. Resistivity models constructed from field data were highly dependent on the norm used. Simulations that used the root mean square percentage error as the norm significantly underestimated the voltage potentials measured near the source pair. This is attributed to the fact that voltage potentials measured at large dipole separations can potentially be given a higher weight as the residual is normalized by the true value, which can be small for large arrays. Simulations using the root mean square error (RMSE) as the norm produced 1D resistivity models whose response better matched the voltage potentials derived from low dipole separations. The RMSE heavily penalizes larger residuals, thus, the RMSE simulations provided solutions whose responses better match observations calculated at small dipole separations (larger voltage potentials) as more importance was placed on matching larger voltage measurements. The significance of this research in regards to advancing geophysical inversion techniques is two fold. The first significant contribution is that the numerical accuracy of AEM solutions are not dependent upon the discretization of a computational grid, thus, a complex discretization is not required to achieve a sound hydrogeologic interpretation of ERT data unless necessitated by the data. Although the earth is inherently complex, a finely discretized model leads to a large number of parameters that need to be estimated. An equally good explanation of the subsurface may be provided by analytic elements, removing the requirement of finely discretized regions to achieve numerical stability. The second major contribution is that the RMSE or MAE should be used as the norm for models using a single objective function to provide the most realistic representation of earth models. Ultimately, the AEM-PSO scheme improves the hydrogeologic information that can be inferred from ERT data, and furthers the ability of ERT to serve as an effective in situ hydrogeologic characterization method.

Cited by 0

AN APPLICATION OF THE ANALYTIC ELEMENT METHOD IN MODELING FLORIDA EVERGLADES HYDROLOGY

M. M. Wilsnack, Victor P. Kelson, Jack Wittman · JAWRA Journal of the American Water Resources Association · 2005

ABSTRACT: The large volumes of ground water that are discharged from the Everglades toward the Miami metropolitan area have historically posed a significant environmental water supply problem. In order to analyze the effects of seepage barriers on these subsurface outflows, the analytic element modeling code GFLOW was used to construct a ground water flow model of a region that includes a portion of the Everglades along with adjacent developed areas. The hydrology of this region can be characterized by a highly transmissive surficial aquifer in hydraulic contact with wetlands and canals. Calibration of the model to both wet and dry season conditions yielded satisfactory results, and it was concluded that the analytic element method is a suitable technique for modeling ground water flow in the Everglades environment. Finally, the model was used to evaluate the potential effectiveness of a subsurface barrier approximately two miles long for increasing water levels within the adjacent fringes of the Everglades National Park. It was found that the barrier had a negligible effect on water levels due to both its relatively short length and the high transmissivity of the surficial aquifer.

Cited by 3

A matrix solver approach for fracture flow simulation by Analytic Element Method

Hussain, Sardar Muhammad, Cuminato, José Alberto, Marin, Ivan Silvestre Paganini et al. · RePEc: Research Papers in Economics

The manuscript presents a study on 2D groundwater flow through porous and fractured media employing Analytic Element Method. The approximate solution based on a series expansion is presented for the problem with multiple fractures. Influence of each fracture can be expressed in a series satisfying Laplace’s equation perfectly. The unknown coefficients in series expansion are determined by using the discharge potentials of all the elements linked to them. Dimension, location and conductivities were randomly selected for the inhomogeneities. Furthermore, a matrix method as a direct solver for AEM, obtained by implementing the intern boundary conditions as well as convergence analysis of iterative method of Gauss–Seidel type are also discussed.

Cited by 0

Analytic and Computational Assessment of Locking in the hp Finite Element Method

Manil Suri · 1994

Locking is the phenomenon by which the numerical approximation of parameter-dependent problems deteriorates for values of the parameter close to a limiting value. In this paper, we give a definition of locking and develop precise computable and analytic ways to quantify it. Using the example of nearly incompressible elasticity, we show by means of computational and theoretical results, the difference between the h version and p=hp version in combatting locking. Our results establish the superiority of high order elements (both h; p and hp) when the standard variational form is used. We also discuss other issues such as curved elements, mixed methods, and locking phenomena for problems over anisotropic materials and over thin domains. Key Words: locking, h version, p version, hp version, finite element method To appear in Computer Methods in Applied Mechanics and Engineering, 1995. (1) Research partially supported by the Air Force Office of Scientific Research, Bolling AFB, DC, under G...

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Five-phase Induction Motor Design using an Analytic Method and Finite Element Analysis

Ionuț Vasile, Constantin Dumitru, Emil Tudor et al. · 2023

The induction motor has a history of over 130 years, this vast experience has led to standardized values for many design parameters such as motor size, electric and magnetic properties as well as mechanical and thermal values. The authors propose an algorithm for the optimal design of an induction motor with a squirrel cage rotor with given input data. Based on a number of constraints that can be introduced, the algorithm computes an optimal solution for the sizing of the motor, in terms of geometry details as well as electromagnetic properties. A five-phase induction motor is designed and finite element analysis is performed to test the predicted performances.

Cited by 3