Extension of the Heaslet‐Alksne Technique to arbitrary soil water diffusivities

Parlance, Marc B.; Prasad, S. N.; Parlange, Marc B.; Römkens, M. J. M.

doi:10.1029/92wr01683

Cited by 64 publications

(42 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The Heaslet and Alksne [1961] technique was initially applied to solve the nonlinear diffusion equation with a power law diffusivity and obtained a solution for (z, t) by expansion around the wetting front position. It was found to coincide with the numerical solution of Philip [1955] by Brutsaert and Weizman [1970] and was later extended for arbitrary soil water diffusivities by Prasad and Römkens [1982] and Parlange et al [1984aParlange et al [ , 1992. It was further generalized to include the effects of gravity by Parlange et al [1997], resulting in…”

Section: Space Expansion Approach: the Heaslet And Alksne Methodsmentioning

confidence: 97%

Infiltration into soils: Conceptual approaches and solutions

Assouline

2013

Water Resources Research

222

115

View full text Add to dashboard Cite

[1] Infiltration is a key process in aspects of hydrology, agricultural and civil engineering, irrigation design, and soil and water conservation. It is complex, depending on soil and rainfall properties and initial and boundary conditions within the flow domain. During the last century, a great deal of effort has been invested to understand the physics of infiltration and to develop quantitative predictors of infiltration dynamics. Jean-Yves Parlange and Wilfried Brutsaert have made seminal contributions, especially in the area of infiltration theory and related analytical solutions to the flow equations. This review retraces the landmark discoveries and the evolution of the conceptual approaches and the mathematical solutions applied to the problem of infiltration into porous media, highlighting the pivotal contributions of Parlange and Brutsaert. A historical retrospective of physical models of infiltration is followed by the presentation of mathematical methods leading to analytical solutions of the flow equations. This review then addresses the time compression approximation developed to estimate infiltration at the transition between preponding and postponding conditions. Finally, the effects of special conditions, such as the presence of air and heterogeneity in soil properties, on infiltration are considered.

show abstract

Section: Space Expansion Approach: the Heaslet And Alksne Methodsmentioning

confidence: 97%

Infiltration into soils: Conceptual approaches and solutions

Assouline

2013

Water Resources Research

222

115

View full text Add to dashboard Cite

show abstract

“…Introducing the Boltzmann variable, q~ = xt-1/2, transforms equations (5)- (8) An accurate approximate solution to this nonlinear problem is given by [11]: 2IgD(_D~da=s~+ 2-'A +2 (11) where s is the scaled sorptivity:…”

mentioning

confidence: 99%

Sorptivity and the estimation of water penetration into unsaturated concrete

1999

View full text Add to dashboard Cite

Uptake of water (and therefore ions) by unsaturated, hardened concrete may be characterised by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of concrete resistance to exposure in aggressive environments. The complete process is described by a nonlinear diffusion equation, with the hydraulic diffusivity a strongly nonlinear function of the degree of saturation of the concrete. Accurate analytical approximations to the solution of this equation, as well as numerical solutions for general conditions, exist when the diffusivity function is known. Unfortunately, it is not an easy function to determine, requiring accurate information on the water penetration profile. A simple alternative which estimates the diffusivity from sorptivity and porosity measurements is presented for an assumed exponential dependence of diffusivity on water saturation. Predicted water penetration profiles corresponding to this estimated diffusivity are shown to be accurate by comparison with published experimental results. RESUMg

show abstract

“…According to Parlange [1] , the Boltzmann variable xt φ = is introduced, and Eq. 6 is transformed as [1] ( ) …”

Section: Model Definitionmentioning

confidence: 99%

“…Richards' equation (RE) is a non-linear partial differential equation (PDE) of saturation and can be expressed as [1] () …”

Section: Introductionmentioning

confidence: 99%