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

ABSTRACT

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

¹ Contribution from the Soil and Water Conservation Research Division, ARS, USDA, and the Illinois Agr. Exp. Sta. Supported in part by Research and Marketing Contract No. 12-14-100-5742 (41) between the Board of Trustees of the University of Illinois and the USDA. Presented at a meeting of Div. S-1, Soil Science Society of America, Denver, Colo., Nov. 17–21, 1963.

² Professor of Soil Physics, University of Illinois; Research Soil Scientist, USDA; and Professor of Mathematics, University of Illinois, Urbana, respectively.

Received for publication November 23, 1964. Accepted for publication January 15, 1965.