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research article

Approximate analytical solution of the nonlinear diffusion equation for arbitrary boundary conditions

Parlange, J.-Y.
•
Hogarth, W. L.
•
Parlange, M. B.  
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1998
Transport in Porous Media

A general approximation for the solution of the one- dimensional nonlinear diffusion equation is presented. It applies to arbitrary soil properties and boundary conditions. The approximation becomes more accurate when the soil-water diffusivity approaches a delta function, yet the result is still very accurate for constant diffusivity suggesting that the present formulation is a reliable one. Three examples are given where the method is applied, for a constant water content at the surface, when a saturated zone exists and for a time-dependent surface flux.

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Type
research article
DOI
10.1023/A:1006508721609
Author(s)
Parlange, J.-Y.
Hogarth, W. L.
Parlange, M. B.  
Haverkamp, R.
Barry, D. A.  
Ross, P. J.
Steenhuis, T. S.
Date Issued

1998

Published in
Transport in Porous Media
Volume

30

Issue

1

Start page

45

End page

55

Subjects

Nonlinear diffusion

•

Analytic solutions

•

Exact solutions

•

Approximations

•

Similarity

•

Soil

•

Water

•

Infiltration equation

•

First integrals

•

Sorptivity

•

Soils

•

Flow

•

Porous media

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
ECOL  
EFLUM  
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/221075
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