lnfiltration Simulation in Soils

Abstract

Esaturated soils applying Richard’s equation restricted to vertical flow and having as an unknown the matrix potential. Since soil humidity and hydraulic conductivity are highly non-linear univocal functions of the matrix potential, there is no analytical solution and the equation is solved through a finite-difference implicit scheme that leads to a system of linear equations, which is solved using the Newton-Raphson algorithm and two upper and lower boundary initial conditions. The considered soil  profile must be discritized with n+ 1 elements of dz width, computing for each one of them the hydraulic conductivity at the middle of the element as the average of the conductivities of both the element under consideration and the next one in a downward vertical direction, as well as the discharge as a function of this hydraulic conductivity As many hydraulic functions as available horizons are computed. The system of equations is solved for a maximum number of iterations and, if there is no convergence, the time interval is divided by two, thus repeating the process for the initial values. The algorithm shown is applied to two homogeneous soils and the results are presented. Comparable results are reported by Anlauf et al (1988), but these must be contrasted with measurements.