Application of conformal mapping to two-dimensional flows in an anisotropic aquifer

Nirupam Ghosh (), Timir Karmakar () and G. P. Sekhar ()
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Nirupam Ghosh: Indian Statistical Institute, Statistics and Mathematics Unit
Timir Karmakar: Indian Institute of Technology Kharagpur
G. P. Sekhar: Indian Institute of Technology Kharagpur

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 3, 617-626

Abstract: Abstract Analytic element method plays a crucial role to solve fluid flow problems in porous media having isotropic hydraulic conductivity. Flow problems in anisotropic domains can be modeled by means of an equivalent isotropic domains by appropriate scaling of the coordinate transformation. Once analytic solutions are obtained for the equivalent isotropic domain, they can be mapped back to the original anisotropic domain. In this article we use a suitable coordinate transformation to solve the problem of potential flow in anisotropic domain. If the standard analytic solution for steady radial flow towards a well is considered with coordinate transformation, the resulting solutions correctly models the far field but they do not meet the constant head boundary condition at the boundary of a well. This is a significant drawback if one is interested in the flow field close to the well or wish to estimate the head at the pumping well. In this paper, using conformal mapping, we develop a technique to overcome this difficulty on the boundary of the well.

Keywords: Analytic elementary method; Conformal mappings; Complex potential; Stream function; Anisotropic aquifer; 76M40; 76S05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00153-1

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