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Numerical Solution of the Nonlinear Diffusion Equation for Water Flow in a Horizontal Soil Column of Finite Length
Author(s) -
Klute A.,
Whisler F. D.,
Scott E. J.
Publication year - 1965
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1965.03615995002900040005x
Subject(s) - thermal diffusivity , outflow , inflow , diffusion equation , constant (computer programming) , mathematics , nonlinear system , diffusion , flow (mathematics) , water flow , flux (metallurgy) , water content , thermodynamics , mechanics , physics , materials science , geometry , geotechnical engineering , geology , meteorology , metallurgy , economy , quantum mechanics , computer science , economics , programming language , service (business)
The nonlinear diffusivity form of the flow equation for water in soil was solved numerically subject to the conditions: θ(0, t) = θ b , t > 0; θ(x, 0) = θ s , 0 < x < L; ∂θ/∂x = 0, x = L, t > 0; and D(θ) = αe βθ . In these equations θ is the volume water content, D(θ) is the diffusivity function, α and β are constants, θ b and θ s 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(θ s − θ b ). Both inflow and outflow cases were considered, and the effect of the parameters α and β on the flow behavior is discussed.