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A mixed boundary
value problem in potential theory for a bimaterial porous
region: An application in the environmental geosciences
A. P. S. Selvadurai
Vol. 2 (2014), No. 2, 109–122
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Abstract |
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This paper develops an exact closed-form solution to a mixed boundary value problem in potential theory for an elliptical opening located at an impervious interface separating two dissimilar, nondeformable porous media. The resulting solution provides a convenient result for estimating the leakage rate of an incompressible fluid retained in the system at a hydraulic potential difference. The result for the elliptical opening is also used to provide a Pólya–Szegö-type estimate for leakage rates from openings of arbitrary shape located at the impermeable interface. The extension of the study to include leakage into a transversely isotropic porous medium with the plane of isotropy inclined to the impervious boundary is also discussed. |
Keywords
potential theory, mixed boundary value problem, bimaterial
region, Darcy flow, leakage from barrier, bounds for
leakage rates, transverse isotropic permeability,
mathematical geosciences
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Mathematical Subject Classification 2010
Primary: 31A10
Secondary: 31A25
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Milestones
Received: 7 August 2012
Revised: 13 March 2013
Accepted: 20 April 2013
Published: 9 June 2014
Communicated by Felix Darve
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Authors |
| A. P. S. Selvadurai | |
| Department of Civil Engineering and
Applied Mechanics McGill University Macdonald Engineering Building 817 Sherbrooke Street West Montréal, QC H3A 0C3 Canada |
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