Vol. 2, No. 2, 2014

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ISSN: 2325-3444 (e-only)
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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
Abstract

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
Mathematical Subject Classification 2010
Primary: 31A10
Secondary: 31A25
Milestones
Received: 7 August 2012
Revised: 13 March 2013
Accepted: 20 April 2013
Published: 9 June 2014

Communicated by Felix Darve
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