Comparison of vertical discretization techniques in finite-difference models of ground-water flow; example from a hypothetical New England setting

Harte, Philip T.

doi:10.3133/ofr94343

Cited by 4 publications

(6 citation statements)

References 6 publications

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“…This finite-difference scheme was a two-step explicit approach named predictor-corrector by Mac Cormack (1969), and was conditionally stable and convergent. The second is its use of NHML to properly approximate the sloping base (Harte 1994). To deal with groundwater flow in an unconfined sloping aquifer, the commonly used three-dimensional finitedifference model MODFLOW (McDonald and Harbaugh 1988) can be a powerful tool if one can adequately handle the characteristics of the sloping base.…”

Section: Problems In Existing Solutions Of Unconfined Flow In Slopingmentioning

confidence: 99%

“…The first is its capability to handle the free water table using the rewetting package (Niswonger et al 2011). The second is its use of NHML to properly approximate the sloping base (Harte 1994). In fact, NHML is capable of dealing with variable sloping angles, making it very useful for studying realistic sloping aquifers over a large spatial scale which may see variable sloping angles at different locations.…”

Section: Problems In Existing Solutions Of Unconfined Flow In Slopingmentioning

confidence: 99%

“…The commonly used MODFLOW model (McDonald and Harbaugh 1988) can be employed to deal with unconfined flow in a sloping aquifer if one used a sufficiently large number of layers for vertical discretization to describe the sloping base. To overcome such difficulty, one alternative approach was to use either layers with variable thickness or the so-called nonhorizontal-model-layer (NHML) as specifically discussed by Harte (1994). Firstly, the maximum number of layers used in MODFLOW-2000 (McDonald andHarbaugh 1988) was limited (usually less than 200 in Visual MODFLOW).…”

Section: Introductionmentioning

confidence: 99%

“…As a result, we found that the simulation was either divergent or ended in physically unrealistic results. To overcome such difficulty, one alternative approach was to use either layers with variable thickness or the so-called nonhorizontal-model-layer (NHML) as specifically discussed by Harte (1994). By doing so, one can use very few or even one layer for the vertical discretization, thus substantially reduced the computational cost and avoided the convergence problem as commonly seen in above discretization with horizontal layers.…”

Section: Introductionmentioning

confidence: 99%

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A New Package in MODFLOW to Simulate Unconfined Groundwater Flow in Sloping Aquifers

2013

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The nonhorizontal-model-layer (NHML) grid system is more accurate than the horizontal-model-layer grid system to describe groundwater flow in an unconfined sloping aquifer on the basis of MODFLOW-2000. However, the finite-difference scheme of NHML was based on the Dupuit-Forchheimer assumption that the streamlines were horizontal, which was acceptable for slope less than 0.10. In this study, we presented a new finite-difference scheme of NHML based on the Boussinesq assumption and developed a new package SLOPE which was incorporated into MODFLOW-2000 to become the MODFLOW-SP model. The accuracy of MODFLOW-SP was tested against solution of Mac Cormack (1969). The differences between the solutions of MODFLOW-2000 and MODFLOW-SP were nearly negligible when the slope was less than 0.27, and they were noticeable during the transient flow stage and vanished in steady state when the slope increased above 0.27. We established a model considering the vertical flow using COMSOL Multiphysics to test the robustness of constrains used in MODFLOW-SP. The results showed that streamlines quickly became parallel with the aquifer base except in the narrow regions near the boundaries when the initial flow was not parallel to the aquifer base. MODFLOW-SP can be used to predict the hydraulic head of an unconfined aquifer along the profile perpendicular to the aquifer base when the slope was smaller than 0.50. The errors associated with constrains used in MODFLOW-SP were small but noticeable when the slope increased to 0.75, and became significant for the slope of 1.0.

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Section: Problems In Existing Solutions Of Unconfined Flow In Slopingmentioning

confidence: 99%

Section: Problems In Existing Solutions Of Unconfined Flow In Slopingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Package in MODFLOW to Simulate Unconfined Groundwater Flow in Sloping Aquifers

2013

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“…This is different from the truncation error associated with grid size and contains a component proportional to the deviation of the grid from being orthogonal. The errors induced by conforming grids were previously studied by Weiss (1985), Harte (1994), Hoagland and Pollard (2003), and Bower et al (2004). They concluded that the appropriate grid size could be determined a priori for a given problem.…”

Section: Introductionmentioning

confidence: 97%

An Investigation of Numerical Grid Effects in Parameter Estimation

Zyvoloski

Vesselinov

2006

Groundwater

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Modern ground water characterization and remediation projects routinely require calibration and inverse analysis of large three-dimensional numerical models of complex hydrogeological systems. Hydrogeologic complexity can be prompted by various aquifer characteristics including complicated spatial hydrostratigraphy and aquifer recharge from infiltration through an unsaturated zone. To keep the numerical models computationally efficient, compromises are frequently made in the model development, particularly, about resolution of the computational grid and numerical representation of the governing flow equation. The compromise is required so that the model can be used in calibration, parameter estimation, performance assessment, and analysis of sensitivity and uncertainty in model predictions. However, grid properties and resolution as well as applied computational schemes can have large effects on forward-model predictions and on inverse parameter estimates. We investigate these effects for a series of one- and two-dimensional synthetic cases representing saturated and variably saturated flow problems. We show that "conformable" grids, despite neglecting terms in the numerical formulation, can lead to accurate solutions of problems with complex hydrostratigraphy. Our analysis also demonstrates that, despite slower computer run times and higher memory requirements for a given problem size, the control volume finite-element method showed an advantage over finite-difference techniques in accuracy of parameter estimation for a given grid resolution for most of the test problems.

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Simulations of Flow in Crystalline Rock and Recharge from Overlying Glacial Deposits in a Hypothetical New England Setting

Harte

Winter

1995

Groundwater

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Cross‐sectional, finite‐difference, steady‐state ground‐water‐flow models of a generalized New England landscape were constructed to examine the effects of hydraulic conductivity and topography on bulk‐fluid flow processes in fractured crystalline rock. The generalized landscape consists of a flat hilltop, a hillside that has a slope of 0.17 ft/ft, and a flat river valley. It includes three hydrogeologic units, stratified drift in the river valley, glacial till, and underlying crystalline rock. Distribution of recharge to and discharge from bedrock is affected by the presence of small topographic features, such as terraces on the hillside. Most of these terraces consist partly or entirely of sand, and they create localized areas of recharge to and discharge from bedrock. Maximum recharge to bedrock commonly occurs at downward inflections of the water table, and discharge occurs at upward inflections of the water table. These inflections of the water table are associated with inflections in topography because the shallow depth of water on hilltops and hillsides resemble the configuration of the land surface. Regional ground‐water flow in crystalline rock and distribution of bedrock recharge and discharge are also affected by heterogeneities in hydraulic conductivity of the bedrock. Vertical heterogeneity creates short, shallow flow paths in high‐relief terrain. Horizontal heterogeneity causes large variations in the size of bedrock recharge areas; in some cases the difference from homogeneous conditions is more than 50 percent.

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Comparison of vertical discretization techniques in finite-difference models of ground-water flow; example from a hypothetical New England setting

Cited by 4 publications

References 6 publications

A New Package in MODFLOW to Simulate Unconfined Groundwater Flow in Sloping Aquifers

A New Package in MODFLOW to Simulate Unconfined Groundwater Flow in Sloping Aquifers

An Investigation of Numerical Grid Effects in Parameter Estimation

Simulations of Flow in Crystalline Rock and Recharge from Overlying Glacial Deposits in a Hypothetical New England Setting

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