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This article in SSSAJ

  1. Vol. 29 No. 4, p. 353-358
    Received: Nov 23, 1964
    Accepted: Jan 15, 1965

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Numerical Solution of the Nonlinear Diffusion Equation for Water Flow in a Horizontal Soil Column of Finite Length1

  1. A. Klute,
  2. F. D. Whisler and
  3. E. J. Scott2



The nonlinear diffusivity form of the flow equation for water in soil was solved numerically subject to the conditions: θ(0, t) = θb, t > 0; θ(x, 0) = θs, 0 < x < L; ∂θ/∂x = 0, x = L, t > 0; and D(θ) = αeβθ. In these equations θ is the volume water content, D(θ) is the diffusivity function, α and β are constants, θb and θs are the constant values of boundary and initial water content, and L is the length of the column. The solution θ(x, t) and the flux and cumulative flow across the plane x = 0 were obtained for various values of the parameter β̄ = β(θs − θb). Both inflow and outflow cases were considered, and the effect of the parameters α and β on the flow behavior is discussed.

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