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

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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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Authors and Affiliations

  1. Department of Agricultural and Biological Engineering, Cornell University, Ithaca, NY, 14853, U.S.A.

    J.-Y. Parlange & T. S. Steenhuis

  2. Faculty of Environmental Sciences, Griffith University, Nathan, Brisbane, Queensland, 4111, Australia

    W. L. Hogarth

  3. Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, MD, 21218, U.S.A.

    M. B. Parlange

  4. Laboratoire d'Etude du Transfert en Hydrologie et Environnement (LTHE/IMG, UJF, CNRS URA 1512), BP 53, 38041, Grenoble, France

    R. Haverkamp

  5. Department of Environmental Engineering, Centre for Water Research, University of Western Australia, Nedlands, Western Australia, 6907, Australia

    D. A. Barry

  6. Division of Soils, CSIRO, Davies Laboratory, Townsville, Queensland, 4814, Australia

    P. J. Ross

Authors
  1. J.-Y. Parlange
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  2. W. L. Hogarth
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  3. M. B. Parlange
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  4. R. Haverkamp
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  5. D. A. Barry
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  6. P. J. Ross
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  7. T. S. Steenhuis
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Parlange, JY., Hogarth, W.L., Parlange, M.B. et al. Approximate Analytical Solution of the Nonlinear Diffusion Equation for Arbitrary Boundary Conditions. Transport in Porous Media 30, 45–55 (1998). https://doi.org/10.1023/A:1006508721609

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  • DOI: https://doi.org/10.1023/A:1006508721609

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