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On Solving the Flow Equation in Unsaturated Soils by Optimization: Horizontal Infiltration
Author(s) -
Parlange JeanYves
Publication year - 1975
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/sssaj1975.03615995003900030019x
Subject(s) - sorptivity , infiltration (hvac) , thermal diffusivity , soil water , mathematics , richards equation , vadose zone , numerical analysis , mathematical analysis , invariant (physics) , mathematical optimization , soil science , geotechnical engineering , physics , geology , thermodynamics , porosity , mathematical physics
Recently, integral methods have been developed that provide accurate approximations to the diffusion equation with rapidly varying diffusivity, but require in general some numerical iteration. In the present paper, a new analytical approach is developed which yields optimal approximations without any numerical iteration. The method is applied to the problem of one‐dimensional horizontal infiltration of water in soils. In that case it is shown that the sorptivity is an invariant, which can be expressed in terms of the sum of two integrals involving the diffusivity. The analytical results are in excellent agreement with numerical calculations for Yolo light clay.