Approximate Analytical Solution of the Nonlinear Diffusion Equation for Arbitrary Boundary Conditions

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Author(s)
Parlange, JY
Hogarth, WL
Parlange, MB
Haverkamp, R
Barry, DA
Ross, PJ
Steenhuis, TS
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1998
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Abstract

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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Transport in Porous Media

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30

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1

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Applied mathematics

Chemical engineering

Civil engineering

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