The method of images for leaky boundaries

✍ Scribed by Erik I. Anderson

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 352 KB
• Volume: 23
• Category: Article
• ISSN: 0309-1708
• DOI: 10.1016/s0309-1708(99)00044-5

✦ Synopsis

An analytic solution is presented describing ¯ow to a drain in a semi-in®nite domain bounded by a leaky layer of constant thickness. The solution is developed by applying the method of images to two parallel boundaries: an inhomogeneity boundary and an equipotential boundary. It is then demonstrated that the solution for the problem with the leaky layer approximated by a leaky boundary (a mixed boundary condition) may be obtained by allowing the thickness, h à , and the hydraulic conductivity, k à , of the leaky layer to vanish while holding the ratio h à ak à constant. A method of images for leaky boundaries is proposed, in which a drain is imaged with respect to a leaky boundary by an image drain and an image line dipole. The method of images for a leaky boundary is applied to solve the problem of ¯ow to a horizontal drain in a semi-con®ned aquifer.