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Transport in Porous Media

, Volume 30, Issue 1, pp 45–55 | Cite as

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

  • J.-Y. Parlange
  • W. L. Hogarth
  • M. B. Parlange
  • R. Haverkamp
  • D. A. Barry
  • P. J. Ross
  • T. S. Steenhuis
Article

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.

nonlinear diffusion analytic solutions exact solutions approximations similarity 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • J.-Y. Parlange
    • 1
  • W. L. Hogarth
    • 2
  • M. B. Parlange
    • 3
  • R. Haverkamp
    • 4
  • D. A. Barry
    • 5
  • P. J. Ross
    • 6
  • T. S. Steenhuis
    • 1
  1. 1.Department of Agricultural and Biological EngineeringCornell UniversityIthacaU.S.A.
  2. 2.Faculty of Environmental SciencesGriffith University, NathanBrisbaneAustralia
  3. 3.Department of Geography and Environmental EngineeringJohns Hopkins UniversityBaltimoreU.S.A.
  4. 4.Laboratoire d'Etude du Transfert en Hydrologie et Environnement (LTHE/IMG, UJF, CNRS URA 1512)GrenobleFrance
  5. 5.Department of Environmental Engineering, Centre for Water ResearchUniversity of Western AustraliaNedlandsAustralia
  6. 6.Division of Soils, CSIRO, Davies LaboratoryTownsvilleAustralia

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