Saturated-Unsaturated 3D Groundwater Model. I: Development

Doğan, A. Umran; Motz, Louis H.

doi:10.1061/(asce)1084-0699(2005)10:6(492)

Cited by 53 publications

(30 citation statements)

References 18 publications

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“…[39]. There are numerous methods suggested in the literature for computing the intercell average of the relative permeabilities between grid cells in the discretized equation [40] . In general, the mean hydraulic conductivity between grid cells can be estimated using the distance-weighted arithmetic mean for unsaturated zone and the weighted harmonic mean for saturated zone, if the relatively fine space-time meshes are used.…”

Section: Numerical Solution Methodsmentioning

confidence: 99%

A physically-based integrated numerical model for flow, upland erosion, and contaminant transport in surface-subsurface systems

2009

Sci. China Ser. E-Technol. Sci.

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This paper presents a physically-based integrated hydrologic model that can simulate the rainfall-induced 2D surface water flow, 3D variably saturated subsurface flow, upland soil erosion and transport, and contaminant transport in the surface-subsurface system of a watershed. The model couples surface and subsurface flows based on the assumption of continuity conditions of pressure head and exchange flux at the ground, considering infiltration and evapotranspiration. The upland rill/interrill soil erosion and transport are simulated using a non-equilibrium transport model. Contaminant transport in the integrated surface and subsurface domains is simulated using advection-diffusion equations with mass changes due to sediment sorption and desorption and exchanges between two domains due to infiltration, diffusion, and bed change. The model requires no special treatments at the interface of upland areas and streams and is suitable for wetland areas and agricultural watersheds with shallow streams.

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Section: Numerical Solution Methodsmentioning

confidence: 99%

A physically-based integrated numerical model for flow, upland erosion, and contaminant transport in surface-subsurface systems

2009

Sci. China Ser. E-Technol. Sci.

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“…The solution is then obtained using, for example, finite difference [7,8] or finite element methods [9]. A drawback with this approach is the nonlinearity of Richards' equation which results in a substantial computational cost to obtain a solution.…”

Section: Introductionmentioning

confidence: 99%

Efficient water table evolution discretization using domain transformation

et al. 2016

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Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem is greatly simplified by using a mapping from the physical domain to a reference domain and is then further reduced to a single, (nonlinear) partial differential equation. We show well-posedness of the approach and propose a stable and convergent discretization scheme. Numerical results are presented supporting the theory.

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“…The finite difference model has distinct advantages over other models because of its simplicity of discretization; further, this mode is easy to interpret and code. The finite difference model has been widely used for simulating saturated‐unsaturated flow [ Freeze , 1971; Cooley , 1971; Dane and Mathis , 1981; Haverkamp and Vauclin , 1981; Clement et al , 1994; Weeks et al , 2004; Dogan and Motz , 2005]. However, finite difference do not give an accurate representation of geometrically complex flow domains with low resolution, especially in multidimensional simulations.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional finite difference saturated‐unsaturated flow modeling with nonorthogonal grids using a coordinate transformation method

Ichikawa

Tachikawa

et al. 2010

Water Resources Research

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[1] Study of the saturated-unsaturated flow in porous media is of interest in many branches of science and engineering. Among the various numerical simulation methods available, the finite difference method is advantageous because it offers simplicity of discretization. This method has been widely used for simulating saturated-unsaturated flows. However, the simulation of geometrically complex flow domains requires the use of high-resolution grids in conventional finite difference models because conventional finite difference discretization assumes an orthogonal coordinate system. This makes a finite difference model computationally less efficient than other numerical models that can treat nonorthogonal grids, such as the finite element model and finite volume model. To overcome this disadvantage, we use a coordinate transformation method and develop a multidimensional finite difference model for simulating saturated-unsaturated flows; this model can treat nonorthogonal grids. The cross-derivative terms derived by the coordinate transformation method are evaluated explicitly for ease of coding. Therefore, a 7 point stencil is used for implicit terms in the iterative calculation, as in the case of conventional finite difference models with an orthogonal grid. We assess the performance of the proposed model by carrying out test simulations. We then compare the simulation results with dense grid solutions in order to evaluate the numerical accuracy of the proposed model. To examine the performance of the proposed model, we draw a comparison between the simulation results obtained using the proposed model and the results obtained by using (1) a model in which all terms are considered fully implicitly, (2) a finite element model, and (3) a conventional finite difference model with a highresolution orthogonal grid.Citation: An, H., Y. Ichikawa, Y. Tachikawa, and M. Shiiba (2010), Three-dimensional finite difference saturated-unsaturated flow modeling with nonorthogonal grids using a coordinate transformation method, Water Resour.

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Saturated-Unsaturated 3D Groundwater Model. I: Development

Cited by 53 publications

References 18 publications

A physically-based integrated numerical model for flow, upland erosion, and contaminant transport in surface-subsurface systems

A physically-based integrated numerical model for flow, upland erosion, and contaminant transport in surface-subsurface systems

Efficient water table evolution discretization using domain transformation

Three‐dimensional finite difference saturated‐unsaturated flow modeling with nonorthogonal grids using a coordinate transformation method

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