1973
DOI: 10.1029/wr009i004p01094
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Analytic solution of spatially discretized groundwater flow equations

Abstract: 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[do/dt] • • = O, where R and G are square matrices, o and • 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 • are constant. An analytic solution to the… Show more

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Cited by 22 publications
(11 citation statements)
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“…Several authors have applied the eigenvalue technique as approach to obtain the dynamic response of linear aquifer systems (e.g. Kuiper, 1973;Rai et al, 1998;Sloan, 2000). In the Eigenvalue Method (Sahuquillo, 1983a), the linear differential groundwater flow equation is solved explicitly and continuously in time.…”
Section: Introductionmentioning
confidence: 99%
“…Several authors have applied the eigenvalue technique as approach to obtain the dynamic response of linear aquifer systems (e.g. Kuiper, 1973;Rai et al, 1998;Sloan, 2000). In the Eigenvalue Method (Sahuquillo, 1983a), the linear differential groundwater flow equation is solved explicitly and continuously in time.…”
Section: Introductionmentioning
confidence: 99%
“…Another alternative to define a management model is to include other approaches to solving groundwater flow within the constraints, such as the equations derived from the Eigenvalue Method [ Sahuquillo , 1983a; Andreu and Sahuquillo , 1987]. Several authors have applied eigenvalue techniques as an approach to solving the groundwater flow in linear aquifer systems [e.g., Kuiper , 1973; Rai et al , 1998; Sloan , 2000; Pulido‐Velázquez et al , 2006]. Discretizing the spatial domain, the Eigenvalue Method provides a numerical technique for defining distributed‐parameter models of groundwater flow formulated with an explicit continuous‐in‐time state equation.…”
Section: Introductionmentioning
confidence: 99%
“…Note that hereafter any index in parenthesis, as ( p) in Equation (10), indicates that no summation should be assumed for this index.…”
Section: General Methodology To Solve the Steady Groundwater Flow Equmentioning
confidence: 99%