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Exact Solution for Two‐Dimensional Flow to a Well in an Anisotropic Domain
Author(s) -
Fitts Charles R.
Publication year - 2005
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2005.00082.x
Subject(s) - conformal map , coordinate system , isotropy , mathematical analysis , flow (mathematics) , constant (computer programming) , anisotropy , radius , head (geology) , boundary (topology) , boundary value problem , mathematics , field (mathematics) , domain (mathematical analysis) , transformation (genetics) , physics , geometry , computer science , geology , optics , computer security , geomorphology , programming language , biochemistry , chemistry , pure mathematics , gene
Although most current applications of the analytic element method are formulated for isotropic hydraulic conductivity, anisotropic domains can be modeled with analytic elements using the well‐known coordinate transformation where one coordinate axis is scaled by the square root of the anisotropy ratio. If the standard analytic solution for steady radial flow to a well is used with this coordinate transformation, the resulting solution correctly models the far field but it does not meet the constant head boundary condition at the well radius. This could be a significant shortcoming if you are interested in the flow field close to the well or want to estimate the head at the pumping well. A new solution for two‐dimensional steady flow to a well in an anisotropic domain is presented. This solution satisfies the governing equations exactly and meets the constant head boundary condition at the well radius exactly. It was derived using a conformal mapping.