Conference paper Open Access

Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

Kuhlman, Kristopher L.; Neuman, Shlomo P.

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<identifier identifierType="URL">https://zenodo.org/record/3537126</identifier>
<creators>
<creator>
<creatorName>Kuhlman, Kristopher L.</creatorName>
<givenName>Kristopher L.</givenName>
<familyName>Kuhlman</familyName>
<affiliation>Department of Hydrology and Water Resources, University of Arizona</affiliation>
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<creator>
<creatorName>Neuman, Shlomo P.</creatorName>
<givenName>Shlomo P.</givenName>
<familyName>Neuman</familyName>
<affiliation>Department of Hydrology and Water Resources, University of Arizona</affiliation>
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<titles>
<title>Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow</title>
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<publisher>Zenodo</publisher>
<publicationYear>2006</publicationYear>
<dates>
<date dateType="Issued">2006-06-18</date>
</dates>
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<alternateIdentifier alternateIdentifierType="doi">10.4122/1.1000000586</alternateIdentifier>
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<relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/dtuproceedings</relatedIdentifier>
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<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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<description descriptionType="Abstract">Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method
(LT-AEM) for transient groundwater flow. LT-AEM solves the modified Helmholtz
equation in Laplace space and back-transforms it to the time domain using a Fourier
Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have
extended the method so it can compute hydraulic head and flow velocity distributions
due to any two-dimensional combination and arrangement of point, line and circular
area sinks and sources, nested circular regions having different hydraulic
parameters, and circular regions with specified head or flux. The strengths of all
sinks and sources, and the specified head and flux values, can all vary with time in
an independent and arbitrary fashion. Initial conditions may vary from one circular
element to another. A solution is obtained by matching heads and normal fluxes inside
and outside each circular element. The effect of each circular element on flow is
expressed in terms of generalized Fourier series which converge rapidly (&amp;lt;10 terms)
in most cases. As there are more matching points than Fourier terms, the matching is
accomplished in Laplace space by least-squares. We illustrate the method by
calculating head and velocity as well as representative particle flow paths through a
distribution of circular inhomogeneities and transient sources and sinks.  The
results are compared to a MODFLOW simulation.  We are presently extending the method
to ellipses in two dimensions and spheroids in three dimensions.</description>
<description descriptionType="Other">Presenters:
name: Kuhlman, Kristopher L.
affiliation: Department of Hydrology and Water Resources, University of Arizona</description>
</descriptions>
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