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dc.contributor.advisorNeuman, Shlomo P.en_US
dc.contributor.authorKuhlman, Kristopher Leeen_US
dc.creatorKuhlman, Kristopher Leeen_US
dc.date.accessioned2011-12-05T22:00:27Z
dc.date.available2011-12-05T22:00:27Z
dc.date.issued2008en_US
dc.identifier.urihttp://hdl.handle.net/10150/193735
dc.description.abstractThe 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.
dc.language.isoENen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.subjectanalytic elementen_US
dc.subjectlaplace transformen_US
dc.subjecttransient groundwater flowen_US
dc.subjectelliptical coordinatesen_US
dc.subjecteigenfunction expansionen_US
dc.titleLaplace Transform Analytic Element Method for Transient Groundwater Flow Simulationen_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.contributor.chairNeuman, Shlomo P.en_US
dc.identifier.oclc659749691en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.contributor.committeememberWarrick, Arthur W,en_US
dc.contributor.committeememberHsieh, Paul A.en_US
dc.contributor.committeememberFerre, Ty P. A.en_US
dc.contributor.committeememberGanapol, Barry D.en_US
dc.contributor.committeememberChan, Choliken_US
dc.identifier.proquest2686en_US
thesis.degree.disciplineHydrologyen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.namePhDen_US
refterms.dateFOA2018-06-19T01:43:59Z
html.description.abstractThe 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.


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