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Approximate analytical solution of the Boussinesq equation with numerical validation
Author(s) -
Hogarth W. L.,
Parlange J. Y.,
Parlange M. B.,
Lockington D.
Publication year - 1999
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/1999wr900197
Subject(s) - hydraulic head , aquifer , head (geology) , boussinesq approximation (buoyancy) , boundary (topology) , mathematical analysis , mathematics , constant (computer programming) , function (biology) , exact solutions in general relativity , geology , geotechnical engineering , mechanics , groundwater , computer science , physics , heat transfer , natural convection , geomorphology , evolutionary biology , rayleigh number , biology , programming language
A new approximate solution of the one‐dimensional Boussinesq equation is presented for a semi‐infinite aquifer when the hydraulic head at the source is an arbitrary function of time. Estimates for recharge, discharge, and elevation of the water table are given. The simplicity and accuracy of the approximation are compared with “exact” numerical and analytical solutions. The method of solution is illustrated with several examples including the commonly treated case of a constant boundary head and a nonmonotonically varying boundary head.