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# 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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{
"DOI": "10.4122/1.1000000585",
"title": "Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow",
"issued": {
"date-parts": [
[
2006,
6,
18
]
]
},
"abstract": "Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method\n(LT-AEM) for transient groundwater flow. LT-AEM solves the modified Helmholtz\nequation in Laplace space and back-transforms it to the time domain using a Fourier\nSeries numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have\nextended the method so it can compute hydraulic head and flow velocity distributions\ndue to any two-dimensional combination and arrangement of point, line and circular\narea sinks and sources, nested circular regions having different hydraulic\nparameters, and circular regions with specified head or flux. The strengths of all\nsinks and sources, and the specified head and flux values, can all vary with time in\nan independent and arbitrary fashion. Initial conditions may vary from one circular\nelement to another. A solution is obtained by matching heads and normal fluxes inside\nand outside each circular element. The effect of each circular element on flow is\nexpressed in terms of generalized Fourier series which converge rapidly (&lt;10 terms)\nin most cases. As there are more matching points than Fourier terms, the matching is\naccomplished in Laplace space by least-squares. We illustrate the method by\ncalculating head and velocity as well as representative particle flow paths through a\ndistribution of circular inhomogeneities and transient sources and sinks.  The\nresults are compared to a MODFLOW simulation.  We are presently extending the method\nto ellipses in two dimensions and spheroids in three dimensions.",
"author": [
{
"family": "Kuhlman, Kristopher L."
},
{
"family": "Neuman, Shlomo P."
}
],
"id": "3537126",
"note": "Presenters:\nname: Kuhlman, Kristopher L.\naffiliation: Department of Hydrology and Water Resources, University of Arizona",
"event-place": "Ingeni\u00f8rhuset (Kalvebod Brygge 31-33, 1780 Copenhagen V, Denmark)",
"type": "paper-conference",
"event": "XVI International Conference on Computational Methods in Water Resources (CMWRXVI)"
}
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