Series solutions for flow in stratified aquifers with natural geometry

Wong, Susanna; Craig, James R.

doi:10.1016/j.advwatres.2009.10.006

Cited by 12 publications

(8 citation statements)

References 11 publications

(20 reference statements)

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“…Flow rates are calculated as the spatial derivative of the discharge potential. In a manner similar to Wong and Craig [] for the 2‐D discharge magnitude normal to an interface, the 3‐D discharge across an interface can be decomposed into vertical and horizontal components when the cosine of the slope angle (in both x and y directions) describing each evaluation surface may be approximated as unity. The resulting equation is as follows:

\frac{\partial ϕ_{m}}{\partial η} = \frac{\partial ϕ_{m}}{\partial z} - \frac{d \hat{z}}{d x} \frac{\partial ϕ_{m}}{\partial x} - \frac{d \hat{z}}{d y} \frac{\partial ϕ_{m}}{\partial y}

where η is the coordinate normal to interface surfaces represented by the function

\hat{z} (x, y)

, which is either a layer interface

true(z_{m} (x, y) true)

, bottom bedrock surface

true(z_{M + 1} (x, y) true)

or top interface

true(z_{t} (x, y) true)

.…”

Section: General Problem Statement and Mathematical Formulationmentioning

confidence: 99%

“…Recent advances in semianalytical series solution methods have relaxed the constraints on system geometry. This has been achieved by augmenting the method of separation of variables with a simple least squares numerical algorithm to develop 2‐D homogenous [e.g., Read and Volker , ; Wörman et al ., ] and multilayer [e.g., Craig , ; Wong and Craig , ] topography‐driven flow models. In the topography‐driven flow model the water table location is presumed known prior to the solution as a subdued replica of topographic surface.…”

Section: Introductionmentioning

confidence: 99%

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Semianalytical series solutions for three-dimensional groundwater-surface water interaction

Ameli

Craig

2014

Water Resour. Res.

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A semianalytical grid-free series solution method is presented for modeling 3-D steady state free boundary groundwater-surface water exchange in geometrically complex stratified aquifers. Continuous solutions for pressure in the subsurface are determined semianalytically, as is the location of the water table surface. Mass balance is satisfied exactly over the entire domain except along boundaries and interfaces between layers, where errors are shown to be acceptable. The solutions are derived and demonstrated on a number of test cases and the errors are assessed and discussed. This accurate and grid-free scheme can also be a helpful tool for providing insight into lake-aquifer and stream-aquifer interactions. Here it is used to assess the impact of lake sediment geometry and properties on lake-aquifer interactions. Various combinations of lake sediment are considered and the appropriateness of the Dupuit-Forchheimer approximation for simulating lake bottom flux distribution is investigated. In addition, the method is applied to a test problem of surface seepage flows from a complex topographic surface; this test case demonstrated the method's efficacy for simulating physically realistic domains.

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\frac{\partial ϕ_{m}}{\partial η} = \frac{\partial ϕ_{m}}{\partial z} - \frac{d \hat{z}}{d x} \frac{\partial ϕ_{m}}{\partial x} - \frac{d \hat{z}}{d y} \frac{\partial ϕ_{m}}{\partial y}

where η is the coordinate normal to interface surfaces represented by the function

\hat{z} (x, y)

, which is either a layer interface

true(z_{m} (x, y) true)

, bottom bedrock surface

true(z_{M + 1} (x, y) true)

or top interface

true(z_{t} (x, y) true)

.…”

Section: General Problem Statement and Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semianalytical series solutions for three-dimensional groundwater-surface water interaction

Ameli

Craig

2014

Water Resour. Res.

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“…The method outlined here is quite simple in comparison; it requires no conformal mapping of the domain onto the boundary of the shape, no special far‐field expansion to account for numerical stability issues, and the functional form of the solution is simply expressed in terms of two polynomial series. The elements derive from recent success in modeling features with arbitrary geometry in finite domains using series solution approaches (Wong and Craig ; Ameli and Craig ).…”

Section: Introductionmentioning

confidence: 99%

Closed Analytic Elements with Flexible Geometry

Ranjram¹,

Craig

2018

Groundwater

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A simple and fast treatment of hydrogeologic features with irregularly shaped boundaries in two-dimensional analytic element groundwater flow models is presented. The star domain shapes of the features are restricted to closed shapes represented as smooth and continuous single-valued functions of distance from a focus point, rˆθ . The element can be used to treat a variety of boundary and continuity conditions, including those of irregularly shaped lakes or heterogeneities in hydraulic conductivity. The new element is demonstrated via some simple illustrative test cases and shown to be efficient, accurate, and much simpler to implement than existing solutions for irregular shapes.

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“…The AEM is based on analytic solutions of the groundwater governing equations and does not depend on domain discretization, being able to tackle multiscale problems where other methods have difficulties (MARIN, 2011;STRACK, 1989). This method has been applied in different fields such as wellhead protection area delineation, nuclear waste repositories, and vertical stratified aquifers (MARIN, 2011;WONG;CRAIG, 2010). In this method, each analytic solution represents an hydrogeologic feature.…”

Section: Introductionmentioning

confidence: 99%

Simulation of groundwater flow by the analytic element method

Hussain¹

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Series solutions for flow in stratified aquifers with natural geometry

Cited by 12 publications

References 11 publications

Semianalytical series solutions for three-dimensional groundwater-surface water interaction

Semianalytical series solutions for three-dimensional groundwater-surface water interaction

Closed Analytic Elements with Flexible Geometry

Simulation of groundwater flow by the analytic element method

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