FINITE-DIFFERENCE SOLUTIONS OF THE INFILTRATION EQUATION

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Abstract
An accurate, two-term solution of Richards' equation for one-dimensional, vertical infiltration was obtained by a finite difference, iterative method (FINDIT). Wetting distances and soil water content distributions closely resemble those obtained by Philip with his series solution, which is extremely accurate at short times but fails to converge for long times. Solutions appear to be equally accurate for all times using the proposed procedure. Hence, the proposed procedure does not require additional approximations or matching factors to link separate analyses for short or long infiltration times. Because the solution equation consists of only two terms, the inflow is logically partitioned into matric and gravitational components. The matric component is expressed in a constant sorptivity term S, conceptually identical to the sorptivity S of Philip. The gravitational component is time-dependent and increases to a maximum value equal to the hydraulic conductivity at the soil surface as time approaches infinity. After appropriate coefficients have been determined, both matric and gravitational components of cumulative infiltration may be expressed independently by a logarithmic relationship that avoids the use of D and K functions and iterative computer procedures. An accurate, two-term solution of Richards' equation for one-dimensional, vertical infiltration was obtained by a finite difference, iterative method (FINDIT). Wetting distances and soil water content distributions closely resemble those obtained by Philip with his series solution, which is extremely accurate at short times but fails to converge for long times. Solutions appear to be equally accurate for all times using the proposed procedure. Hence, the proposed procedure does not require additional approximations or matching factors to link separate analyses for short or long infiltration times. Because the solution equation consists of only two terms, the inflow is logically partitioned into matric and gravitational components. The matric component is expressed in a constant sorptivity term S, conceptually identical to the sorptivity S of Philip. The gravitational component is time-dependent and increases to a maximum value equal to the hydraulic conductivity at the soil surface as time approaches infinity. After appropriate coefficients have been determined, both matric and gravitational components of cumulative infiltration may be expressed independently by a logarithmic relationship that avoids the use of D and K functions and iterative computer procedures. © Williams & Wilkins 1982. All Rights Reserved.

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