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Steady Groundwater Flow with Steep Gradients: An Analytic Approach to the 2D–Problem with a Vertical Pressure Boundary Condition and Steady Recharge/Drainage
Author(s) -
Fröhner Anja,
Edenhofer Johann,
Schmitz Gerd H.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410264
Subject(s) - aquifer , groundwater recharge , boundary value problem , geology , groundwater flow , conformal map , flow (mathematics) , groundwater , mechanics , boundary (topology) , drainage , mathematics , geotechnical engineering , geometry , mathematical analysis , physics , ecology , biology
Steady groundwater flow with steep gradients in a vertical plane due to superficial recharge/drainage, inner sources/sinks and a one‐sided pressure boundary condition can be described by a 2D Poisson equation with a nonlinear free surface boundary condition. By means of conformal mapping techniques Schmitz and Edenhofer [1] derived the exact explicit solution of this problem in a horizontally infinite aquifer. Their results are extended to problems with a one‐sided vertical pressure boundary condition, modelling f. ex. the boundary between an aquifer and an adjacent free water body. According to ist simple parametrization, this approach can be applied on one hand to model various real world phenomena like river–aquifer–systems. It may on the other hand serve as a tool for investigating the exactness of numerical solutions and the range of validity of simplifying assumptions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)