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Analytic solution of spatially discretized groundwater flow equations
Author(s) -
Kuiper L. K.
Publication year - 1973
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/wr009i004p01094
Subject(s) - aquifer , mathematics , discretization , matrix (chemical analysis) , constant (computer programming) , groundwater flow , flow (mathematics) , computation , water table , mathematical analysis , groundwater , geometry , geology , geotechnical engineering , chemistry , algorithm , computer science , chromatography , programming language
The Galerkin procedure when it is applied to the equation for horizontal two‐dimensional flow of groundwater in a nonhomogeneous isotropic aquifer generates approximating equations of the following form: Rc + G [ dc/dt ] + f = 0, where R and G are square matrices, c and f are column matrices, and t is time. This matrix equation is decoupled and solved for the unknown column matrix c ( t ). In the case of a confined aquifer that approaches a steady state solution, R , G , and f are constant. An analytic solution to the matrix equation for c ( t ) is given for this case. In the case of a water table aquifer that approaches a steady state solution, R and f are explicitly dependent on c ( t ), and G is constant. For this case, c ( t = ∞) is found in a simple iterative manner, and an iterative procedure is given to approximate c ( t ). These methods are compared with the approximate numerical Crank‐Nicholson procedure by applying both to a particular problem for which the unknown column matrix c ( t ) has 49 elements. The Crank‐Nicholson procedure is found usually to require less computation time to evaluate c ( t ) for the confined aquifer case but to give errors for drawdown averaging approximately 10%. The Crank‐Nicholson procedure is found to take considerably more computation time to evaluate c ( t =∞) for both the confined and the water table cases but to take considerably less time to evaluate c ( t ) for the water table case.