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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

  1. Anja Fröhner1,*,
  2. Johann Edenhofer2,
  3. Gerd H. Schmitz1

Article first published online: 22 DEC 2004

DOI: 10.1002/pamm.200410264

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PAMM

PAMM

Volume 4, Issue 1, pages 566–567, December 2004

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How to Cite

Fröhner, A., Edenhofer, J. and Schmitz, G. H. (2004), Steady Groundwater Flow with Steep Gradients: An Analytic Approach to the 2D–Problem with a Vertical Pressure Boundary Condition and Steady Recharge/Drainage. Proc. Appl. Math. Mech., 4: 566–567. doi: 10.1002/pamm.200410264

Author Information

  1. 1

    Institut für Hydrologie und Meteorologie, TU Dresden, 01062 Dresden

  2. 2

    Zentrum Mathematik M1, TU München, Boltzmannstr. 3, 85748 Garching

*Phone: +49 351 463 34327, Fax: +49 351 463 37162

Publication History

  1. Issue published online: 22 DEC 2004
  2. Article first published online: 22 DEC 2004

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Abstract

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)

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