NUMERICAL STUDY OF QUASI-ANALYTIC AND FINITE-DIFFERENCE SOLUTIONS OF SOIL-WATER TRANSFER EQUATION

The special case of horizontal infiltration of water into a dry soil is utilized to study the problem of using standard finite differencing with an economic grid refinement to locate the wetting front accurately. The procedure used to determine an average value on grid subintervals for the strongly concentration-dependent soil-water diffusivity is identified as being a critical factor in accurately approximating the moisture profile. New averaging techniques are proposed, which are shown to locate the steep front with significantly more accuracy. The exact solution is required as a basis for this study. To meet this need, a quasi-analytic technique is introduced, and is shown to be effective through numerical experiments and comparison with an alternative scheme. © 1978 The Williams & Wilkins Co.