Approximate Analytical Solution of the Nonlinear Diffusion Equation for Arbitrary Boundary Conditions
Parlange, J.-Y. ; Hogarth, W. L. ; Parlange, M. B. ; Haverkamp, R. ; Barry, D. A. ; Ross, P. J. ; Steenhuis, T. S.
Springer
Published 1998
Springer
Published 1998
ISSN: |
1573-1634
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Keywords: |
nonlinear diffusion ; analytic solutions ; exact solutions ; approximations ; similarity
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Source: |
Springer Online Journal Archives 1860-2000
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Topics: |
Geosciences
Technology
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Notes: |
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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Type of Medium: |
Electronic Resource
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URL: |