Ground water flow with free boundaries using the hodograph method

Mark Bakker*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)


A new procedure is presented to obtain exact solutions to groundwater flow problems with free boundaries in the vertical plane. The solution procedure makes use of the hodograph method in combination with conformal mapping. The complex discharge function and the reference function are used as auxiliary functions. The function that maps the upper half plane onto the domain in the complex discharge plane is obtained by integration of the differential equation of Schwarz. The final solution is a linear combination of infinite series and consists of two functions: the conformal map of the upper half plane onto the physical plane and onto the complex potential plane. As an example, the problem of flow over a horizontal base to a straight seepage face is solved. Flow nets are presented for two inclinations of the seepage face and rules are derived for the specification of boundary conditions along seepage faces in Dupuit-Forchheimer models.
Original languageEnglish
Pages (from-to)207-216
Number of pages10
JournalAdvances in Water Resources
Issue number4
Publication statusPublished - 1997
Externally publishedYes


  • Conformal mapping
  • Free boundary problems
  • Groundwater
  • Hodograph method
  • Seepage face


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