Some Integral and Closed Form Analytical Solutions to the Transport Contaminant Equation Considering 3-D Advection & Dispersion

Even though numerical procedures have been enormously enhanced over the last years, analytical closed-form solutions are of special interest to water resources scientists. In general, these solutions are used to check the consistency and validate numerical routines. Bibliographical research reveals...

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Bibliographic Details
Published in:International journal of geomechanics 2012-08
Main Authors: Ozelim, Luan Carlos de SM, Cavalcante, Andre Luis Brasil
Format: Article
Language:English
Subjects:
Advection
Contaminants
Dispersion
Exact solutions
Integrals
Mathematical analysis
Mathematical models
Online Access:Get full text
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Summary:Even though numerical procedures have been enormously enhanced over the last years, analytical closed-form solutions are of special interest to water resources scientists. In general, these solutions are used to check the consistency and validate numerical routines. Bibliographical research reveals that up-to-date analytical solutions only take into account 1D advection, even when 3D dispersion is considered. This assumption creates an axis dependency since the flux is assumed to be parallel to one of the three possible orthogonal directions, what does not apply to all practical situations, in which diagonal advection is present. In this work an analytical solution is derived for the 3D Advective-Dispersive equation (ADE) by means of Fourier and Laplace integral transforms. The solution allows the contaminant plume to move angularly with respect to the coordinate axes.
ISSN:1532-3641
DOI:10.1061/(ASCE)GM.1943-5622.0000245