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CRITICAL EVALUATION OF CERTAIN METHODS OF UNSTEADY GROUNDWATER HYDRAULICS 1
Author(s) -
Karadi Gabor M.,
Krisek Raymond J.,
Beahea Manual
Publication year - 1970
Publication title -
jawra journal of the american water resources association
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.957
H-Index - 105
eISSN - 1752-1688
pISSN - 1093-474X
DOI - 10.1111/j.1752-1688.1970.tb00492.x
Subject(s) - discretization , groundwater flow equation , mathematics , laplace's equation , steady state (chemistry) , linearization , laplace transform , hydraulics , flow (mathematics) , partial differential equation , interval (graph theory) , groundwater flow , nonlinear system , mathematical analysis , groundwater , geology , aquifer , geometry , geotechnical engineering , physics , chemistry , quantum mechanics , combinatorics , thermodynamics
The basic theories and fundamental assumptions usually employed in the solution of unsteady groundwater flow problems are reviewed critically. The best known method of analysis for such problems is based on the Dupuit‐Forchheimer approximation and leads to a nonlinear parabolic differential equation which is generally solved by linearization or numerical methods. The accuracy of the solution to this equation can be improved by use of a different approach which does not employ the Dupuit Forchheimer assumption, but rather is based on a semi‐numerical solution of the Laplace equation for quasi‐steady conditions. The actual unsteady process is replaced by a sequence of steady‐state conditions, and it is assumed that the actual unsteady flow characteristics during a short time interval can be approximated by those associated with “average” steady state flow. The Laplace equation is solved by a semi‐discretization method according to which the horizontal coordinate is divided into subintervals, while the vertical coordinate is maintained continuous. The proposed method is applied to a typical tile drainage problem, and, based on a comparison of calculated results with experimental data, the method is evaluated and practical conclusions regarding its applicability are advanced.