General Validity of Conductivity Means in Unsaturated  Flow Models

Baker, Donald L.

doi:10.1061/(asce)1084-0699(2006)11:6(526)

Cited by 14 publications

(24 citation statements)

References 6 publications

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“…As listed in Table 3, k app derived from the mean k were widely used and tested in vertical unsaturated flow by Haverkamp and Vauclin (1979), Warrick (1991), Baker (1995Baker ( , 2006, and Belfort and Lehmann (2005). Moreover, k app obtained from mean h were also used and tested by Haverkamp and Vauclin (1979) and Baker (2006), while k app based on the mean S e were rarely used and only the k AM-S was tested by Zaidel and Russo (1992), Miller et al (1998), andWilliams et al (2000).…”

Section: Effects Of K-h-s E Relation Parameters On Distributions Of Kmentioning

confidence: 99%

“…Moreover, k app obtained from mean h were also used and tested by Haverkamp and Vauclin (1979) and Baker (2006), while k app based on the mean S e were rarely used and only the k AM-S was tested by Zaidel and Russo (1992), Miller et al (1998), andWilliams et al (2000). Other two k app derived from the mean S e , k GM-S and k HM-S , were tested for complete comparison purpose in this study.…”

Section: Effects Of K-h-s E Relation Parameters On Distributions Of Kmentioning

confidence: 99%

“…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: Effects Of K-h-s E Relation Parameters On Distributions Of Kmentioning

confidence: 99%

Section: Effects Of K-h-s E Relation Parameters On Distributions Of Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Deficiency of Approximate Interblock Conductivities for Simulation of Horizontal Unsaturated Flow

et al. 2011

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“…The arithmetic mean is used in many studies and models, including the widely accepted HYDRUS model, but it can lead to spurious oscillations in the solution. Various studies [21] indicate that only the upstream mean preserves monotonicity in the solution.…”

Section: Finite Volume Frameworkmentioning

confidence: 99%

Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution

Carbone

Brunetti

Piro

2015

Water

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Abstract:The increasing imperviousness of urban areas reduces the infiltration and evapotranspiration capacity of urban catchments and results in increased runoff. In the last few decades, several solutions and techniques have been proposed to prevent such impacts by restoring the hydrological cycle. A limiting factor in spreading the use of such systems is the lack of proper modelling tools for design, especially for the infiltration processes in a growing medium. In this research, a physically-based model, employing the explicit Finite Volume Method (FVM), is proposed for modelling infiltration into growing media. The model solves a modified version of the Richards equation using a formulation which takes into account the main characteristics of green infrastructure substrates. The proposed model was verified against the HYDRUS-1D software and the comparison of results confirmed the suitability of the proposed model for correctly describing the hydraulic behaviour of soil substrates.

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Why diffusion‐based preconditioning of Richards equation works: Spectral analysis and computational experiments at very large scale

Bertaccini

D'Ambra

Durastante

et al. 2023

Numerical Linear Algebra App

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We consider here a cell‐centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity , a highly nonlinear function, by arithmetic, upstream and harmonic means. The nonlinearities in the equation can lead to changes in soil conductivity over several orders of magnitude and discretizations with respect to space variables often produce stiff systems of differential equations. A fully implicit time discretization is provided by backward Euler one‐step formula; the resulting nonlinear algebraic system is solved by an inexact Newton Armijo–Goldstein algorithm, requiring the solution of a sequence of linear systems involving Jacobian matrices. We prove some new results concerning the distribution of the Jacobians eigenvalues and the explicit expression of their entries. Moreover, we explore some connections between the saturation of the soil and the ill conditioning of the Jacobians. The information on eigenvalues justifies the effectiveness of some preconditioner approaches which are widely used in the solution of Richards equation. We also propose a new software framework to experiment with scalable and robust preconditioners suitable for efficient parallel simulations at very large scales. Performance results on a literature test case show that our framework is very promising in the advance toward realistic simulations at extreme scale.

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General Validity of Conductivity Means in Unsaturated Flow Models

Cited by 14 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

Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution

Why diffusion‐based preconditioning of Richards equation works: Spectral analysis and computational experiments at very large scale

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