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Modeling of Unconfined Ground‐Water Systems
Author(s) -
Murray Willard A.,
Johnson Robert L.
Publication year - 1977
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1977.tb03176.x
Subject(s) - linearization , mathematics , flow (mathematics) , heat equation , linear equation , thermal conduction , yield (engineering) , mathematical analysis , nonlinear system , thermodynamics , geometry , physics , quantum mechanics
Mathematical modeling of regional unconfined ground‐water flow is most often accomplished by using a linearized Dupuit‐Forchheimer (DF) equation. The depth of flow, h, in the general DF equation appears as a squared (h 3 ) term and also as a linear term (h). Linearization of the DF equation is generally accomplished with the first method of linearization presented by Polubarinova‐Kochina (PK), in which h 2 is replaced with h times some average depth of flow. The resulting equation is then linear in h. The second method of linearization described by PK is accomplished by replacing h with h 2 divided by an average flow depth, and hence the resulting equation becomes linear in h 2 . If the second method of linearization is used, the same “heat conduction type” equation is obtained as that from the first method of linearization, but it tends to yield more accurate predictions of water‐table locations. Furthermore, by simply altering the numerical values of boundary condition constants, most existing mathematical models, based on the first method of linearization, can be easily converted to yield solutions to the more accurate equation linearized by the second method.