Numerical Solution of the Nonlinear Diffusion Equation for Water Flow in a Horizontal Soil Column of Finite Length1
- A. Klute,
- F. D. Whisler and
- 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.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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