A Darcian integral approximation to interblock hydraulic conductivity means in vertical infiltration

Baker, Donald L.

doi:10.1016/s0098-3004(99)00129-6

Cited by 20 publications

(25 citation statements)

References 6 publications

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“…A number of estimation methods have been reviewed (Haverkamp and Vauclin 1979;Schnabel and Richie 1984;Warrick 1991;Ross 1990;Zaidel and Russo 1992;Oldenburg and Pruess 1993;Srivastava and Guzman-Guzman 1995;Desbarats 1995;Romano et al 1998;Baker et al 1999;Gastó et al 2002;Brunone et al 2003;Belfort and Lehmann 2005;Baker 1995Baker , 2000Baker , 2006. By assuming constant flux between adjacent blocks, Warrick (1991) first suggested an effective interblock conductivity which was later denoted as k H for the horizontal flow and k V for the vertical flow by Baker (1995).…”

Section: Introductionmentioning

confidence: 99%

“…Desbarats (1995) developed a methodology to calculate k V for flow in heterogeneous media and represented k V as a function of alpha parameter for the constitutive Gardner relationship (Gardner 1958). Baker et al (1999) and Baker (2000Baker ( , 2006 further developed a piecewise as well as an integral approximation to k V using the Brooks-Corey (BC) function (Brooks and Corey 1966). They discussed the general validity of k V in unsaturated flow models.…”

Section: Introductionmentioning

confidence: 99%

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Deficiency of Approximate Interblock Conductivities for Simulation of Horizontal Unsaturated Flow

et al. 2011

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Determination of appropriate horizontal interblock conductivities approximations (k app ) is a critical step for numerical solution of unsaturated flow by finite difference method. This study characterized the horizontal effective interblock conductivity (k H ) and the classical k app by contour map. The deficiencies of the k app were determined by both statistical method and wetting front prediction. Mathematical expressions of the k H were redeveloped for three constitutive hydraulic functions. A large database including ten different k app formulas, three hydraulic functions, and a large range of soil texture is used to determine the deficiencies of the k app for simulation of horizontal unsaturated flow. Some k app may be either higher or lower than the k H since they depend on both the expression forms of the k app and the specific hydraulic functions. For the soil described by the Gardner function, the horizontal wetting front generated from the k H is almost equivalent to the analytical solution, but those predicted from the k app with certain errors. For the soils described by the Brooks-Corey function and the van Genuchten function, the best k app for approximating the k H were also determined, but with conversions for the soils described by the van Genuchten function. For any two k app that hold compatible medians, the k app (>k H ) better tracks the wetting front and makes mass conservation than the k app (

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deficiency of Approximate Interblock Conductivities for Simulation of Horizontal Unsaturated Flow

et al. 2011

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“…In this method the average internodal conductivity is calculated from the Darcy's law assuming steady state flow between two adjacent nodes, which leads to very accurate results. This concept was further developed by Baker [1995, 2000], Baker et al [1999], and Gastó et al [2002], who approximated the Darcian means either as a weighted average of the integrated mean and the conductivity of the upper node or as a weighted average of the two nodal conductivities. The formula of Gastó et al [2002] is simple to implement, but it can be applied neither for an arbitrary type of the conductivity function nor for arbitrary large spatial steps.…”

Section: Introductionmentioning

confidence: 99%

Approximation of internodal conductivities in numerical simulation of one‐dimensional infiltration, drainage, and capillary rise in unsaturated soils

Szymkiewicz

2009

Water Resources Research

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[1] When the unsaturated flow equation is solved with the finite difference method, the water flux between two adjacent nodes of the grid is approximated with a discrete form of Darcy's law. It requires the average value of the hydraulic conductivity in the considered grid block. Since the hydraulic conductivity in unsaturated soil is a highly nonlinear function of the water potential, the nodal conductivities can vary by multiple orders of magnitude, which makes the choice of the appropriate averaging procedure a nontrivial task. In this paper we present a new method to calculate the internodal conductivity for an arbitrary type of the conductivity function and arbitrary large grid size. It is based on the analysis of approximate profiles of the water potential head for steady flow between nodes. Numerical experiments show that the method is reasonably accurate for a wide range of soil types, for both steady and unsteady flow simulations.

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“…Because of its nonlinearity, spatial derivatives of the Richards equation are often evaluated by using internodal hydraulic conductivities, K in ; that is, values of K are estimated from the known hydraulic conductivities at two neighboring nodes of the spatial grid system. Previous studies showed that the accuracy of FD models strongly depends on the weighting technique used for computing K in (Haverkamp and Vauclin, 1979; Zaidel and Russo, 1992; Singh and Bhallamudi, 1998; Baker, 2000). The use of simple arithmetic means has been criticized often, partly because it can cause physical inconsistencies (Haverkamp and Vauclin, 1979; Warrick, 1991a; Baker, 2000).…”

Section: Estimation Of the Finite‐difference Internodal Hydraulic Conmentioning

confidence: 99%

“…Previous studies showed that the accuracy of FD models strongly depends on the weighting technique used for computing K in (Haverkamp and Vauclin, 1979; Zaidel and Russo, 1992; Singh and Bhallamudi, 1998; Baker, 2000). The use of simple arithmetic means has been criticized often, partly because it can cause physical inconsistencies (Haverkamp and Vauclin, 1979; Warrick, 1991a; Baker, 2000). Geometric means as initially proposed by Haverkamp and Vauclin (1979) are now a widely used criterion for evaluating K in = K i+1/2 between two consecutive nodes i and i + 1 of the computational spatial grid:

\begin{matrix} K_{in} = \sqrt{K_{i} K_{i + 1}} \end{matrix}

…”

Section: Estimation Of the Finite‐difference Internodal Hydraulic Conmentioning

confidence: 99%

Numerical Simulations of One‐Dimensional Infiltration into Layered Soils with the Richards Equation Using Different Estimates of the Interlayer Conductivity

Brunone

Ferrante

Romano

et al. 2003

Vadose Zone Journal

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Transient water flow processes in unsaturated soils are usually modeled using the Richards equation. This paper compares several numerical approximations to this equation for vertical infiltration in layered soil profiles. Three formulations of the governing flow equation (i.e., the h‐based, θ‐based, and mixed forms) are compared for the critical test problem of infiltration into a layered soil profile with initially relatively low soil water contents. An efficient, yet relatively simple weighting algorithm is employed that improves the estimation of the interlayer hydraulic conductivity in an h‐based finite‐difference formulation. Results highlight improvements in the mass conservative properties of this model, which is termed the H‐IL model A comparison is then performed between the finite‐difference H‐IL model and a finite‐element model for infiltration toward a water table. The H‐IL model was found to be computationally very efficient for this test problem. For both illustrative flow examples, the different numerical models were evaluated in terms of their ability to reproduce an exact solution developed by Srivastava and Yeh (1991) in their work on one‐dimensional, transient infiltration toward the water table in homogeneous and layered soils.

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A Darcian integral approximation to interblock hydraulic conductivity means in vertical infiltration

Cited by 20 publications

References 6 publications

Deficiency of Approximate Interblock Conductivities for Simulation of Horizontal Unsaturated Flow

Deficiency of Approximate Interblock Conductivities for Simulation of Horizontal Unsaturated Flow

Approximation of internodal conductivities in numerical simulation of one‐dimensional infiltration, drainage, and capillary rise in unsaturated soils

Numerical Simulations of One‐Dimensional Infiltration into Layered Soils with the Richards Equation Using Different Estimates of the Interlayer Conductivity

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