Reply to comment on “On the continuum‐scale modeling of gravity‐driven fingers in unsaturated porous media: The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state” by Mehdi Eliassi and Robert J. Glass

Eliassi, Mehdi; Glass, Robert J.

doi:10.1029/2003wr002053

Cited by 2 publications

(3 citation statements)

References 26 publications

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“…Eliassi and Glass [] argued that this was not an appropriate method of dealing with the relative permeability on a numerical grid. This debate on the numerical modeling brought to the forefront that the entire flow instability, and not just the finger width, was contingent on the exact boundary condition physics [ Eliassi and Glass , ; Braddock and Norbury , ; Deinert et al ., ].…”

Section: Preferential Flow Experimentsmentioning

confidence: 99%

“…One of the main advantages of evaluating the models in terms of overshoot rather than full field preferential flow is that the 1‐D traveling wave nature of the problem lets one break the multidimensional nonlinear partial differential equations down into a nonlinear ordinary differential equation. This greatly simplifies issues with numerical simulation artifacts [ Nieber et al ., ; Eliassi and Glass , ; Braddock and Norbury , ]. The simulated 1‐D profiles can be obtained quickly as a function of the input parameters, and how the models change the effective boundary condition can be determined.…”

Section: Saturation Overshoot Paradigmmentioning

confidence: 99%

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Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

DiCarlo

2013

Water Resources Research

112

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Gravity‐driven multiphase flow in porous media is ubiquitous in the geophysical world; the classic case in hydrology is vertical infiltration of precipitation into a soil. For homogenous porous media, infiltrations are sometimes observed to be stable and laterally uniform, but other times are observed to be unstable and produce preferential flow paths. Since Saffman and Taylor (1958), researchers have attempted to define criteria that determine instability. Saffman and Taylor's analysis consisted of two regions of single phase flow, while Parlange and Hill (1976) integrated this analysis with the multiphase flow equations to provide testable predictions. In the subsequent 40 years, great advances have been made determining the complex interactions between multiphase flow and instability. Theoretically, the stability of the standard multiphase flow equations has been verified, showing the necessity of extensions to the multiphase flow equations to describe the observed unstable flow. Experimentally, it has been shown that the instability is related to a phenomena in 1‐D infiltrations called saturation or pressure overshoot. In this review, the connection between overshoot and instability is detailed, and it is described how models of overshoot can simplify the analysis of current and future models of instability and multiphase flow.

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Section: Preferential Flow Experimentsmentioning

confidence: 99%

Section: Saturation Overshoot Paradigmmentioning

confidence: 99%

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

DiCarlo

2013

Water Resources Research

112

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“…There has been quite a discussion about finger‐like solutions of Richards' equation [see Nieber , 1996; Eliassi and Glass , 2001; Deinert et al , 2003; Eliassi and Glass , 2003, and references therein] modeling flow through an unsaturated homogeneous porous medium subject to constant flux boundary conditions. Nieber [1996] claimed to have produced a finger‐like solution numerically.…”

Section: Introductionmentioning

confidence: 99%

On the incompatibility of Richards' equation and finger‐like infiltration in unsaturated homogeneous porous media

Fürst

Vodák

Šír

et al. 2009

Water Resources Research

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[1] It is demonstrated by means of a mathematical proof that Richards' equation, in principle, cannot admit finger-like solutions for three-dimensional homogeneous unsaturated porous media flow, subject to monotone boundary conditions. This is demonstrated for any reasonable type of homogeneous porous material; the result is not dependent on any particular form of the hydraulic conductivity or the retention curve. Moreover, it is explained why hysteresis of the retention curve does not play any role in the proof. Consequently, the proof is true for any type of hysteretic behavior of the retention curve. An alternative approach to finger flow modeling is discussed which uses the ideas of cellular automata.

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Reply to comment on “On the continuum‐scale modeling of gravity‐driven fingers in unsaturated porous media: The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state” by Mehdi Eliassi and Robert J. Glass

Cited by 2 publications

References 26 publications

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

On the incompatibility of Richards' equation and finger‐like infiltration in unsaturated homogeneous porous media

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