Analytic solution of spatially discretized groundwater flow equations

Kuiper, Logan K.

doi:10.1029/wr009i004p01094

Cited by 22 publications

(11 citation statements)

References 2 publications

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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%

Modeling of stream–aquifer interaction: the embedded multireservoir model

Pulido-Velázquez

Sahuquillo-Herraiz

Ochoa-Rivera

et al. 2005

Journal of Hydrology

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Section: Introductionmentioning

confidence: 99%

Modeling of stream–aquifer interaction: the embedded multireservoir model

Pulido-Velázquez

Sahuquillo-Herraiz

Ochoa-Rivera

et al. 2005

Journal of Hydrology

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“…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%

An efficient conceptual model to simulate surface water body‐aquifer interaction in conjunctive use management models

Pulido-Velázquez

Sahuquillo

Andreu

et al. 2007

Water Resources Research

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[1] In conjunctive use management models, the surface and subsurface components must be simultaneously simulated because of the hydraulic interactions and to the combined operating rules inherent to such schemes. When many management alternatives have to be simulated over long time horizon or when optimizing complex large-scale systems, an efficient tool for surface water body-aquifer interaction simulation is needed. In this paper, we present a parsimonious conceptual model as an alternative approach to simulate aquifer storage and surface water body-aquifer interaction for linear aquifers (linear response of head to stresses). The formulation is deduced from a finite difference model preserving its approach of the geometry, boundary conditions, hydrodynamic parameters (heterogeneity), and spatial distribution of the stresses. It does not require any additional assumption. The solution, obtained using eigenvalue techniques, is formulated with an explicit state equation that is a function of time and does not need to be calculated in a sequential way (that is, time is not discretized). The structure of the solution finally deduced allows a simple conceptual interpretation of surface water body-aquifer interaction phenomenon as the drainage of a number of independent linear reservoirs. The parameters and initial conditions of each linear reservoir are mathematically defined in a univocal way from the original calibrated finite difference model preserving its characteristics. In most practical cases, an accurate solution can be obtained with a reduced number of linear reservoirs. Therefore this multireservoir conceptual definition enables an important reduction in the dimension of the model matrices and provides a straightforward means of incorporating the accuracy of more complex calibrated distributed-parameter numerical models for simulating surface water body-aquifer interaction within conjunctive use management models and with a minimum computational cost. Several case studies (synthetic and real world cases) are used to illustrate the applicability of the methodology.Citation: Pulido-Velazquez, D., A. Sahuquillo, J. Andreu, and M. Pulido-Velazquez (2007), An efficient conceptual model to simulate surface water body-aquifer interaction in conjunctive use management models, Water Resour. Res., 43, W07407,

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“…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%

Solving the steady‐state groundwater flow equation for finite linear aquifers using a generalized Fourier series approach in two‐dimensional domains

Capilla¹,

Pulido-Velázquez²,

Sahuquillo³

et al. 2009

Numerical Meth Engineering

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SUMMARYA method to solve steady linear groundwater flow problems using generalized Fourier Series is developed and particularized for multiple Fourier series in two-dimensional domains. It leads to a linear vector equation whose solution provides a finite number of generalized Fourier coefficients approximating the hydraulic head field. Its implementation is shown and two relevant properties are found for the system matrix. It is always symmetric and, once computed, if additional Fourier terms are needed for a better approximation of the hydraulic head field, previously computed matrix elements remain invariant, i.e. only new rows and columns are added to the system matrix. The method is demonstrated in three simple cases with different geometries and transmissivity fields, where solutions are compared with analytical and finite element method results. Thus, the method is verified as an alternative to other flow solvers. Additionally, it provides a direct way to obtain the spectral form of the flow equation solution, given a spectral representation of transmissivity, and can be easily extended to obtain continuous velocity fields and their approximated spectral expressions.

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Analytic solution of spatially discretized groundwater flow equations

Cited by 22 publications

References 2 publications

Modeling of stream–aquifer interaction: the embedded multireservoir model

Modeling of stream–aquifer interaction: the embedded multireservoir model

An efficient conceptual model to simulate surface water body‐aquifer interaction in conjunctive use management models

Solving the steady‐state groundwater flow equation for finite linear aquifers using a generalized Fourier series approach in two‐dimensional domains

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