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Scaling analysis of Richards equation for horizontal infiltration and its approximate solution
Author(s) -
Wang Ziqing
Publication year - 2021
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 - 10.1002/saj2.20303
Subject(s) - scaling , infiltration (hvac) , ode , mathematics , richards equation , mathematical analysis , exponent , boundary value problem , water content , wetting , power function , geometry , geotechnical engineering , thermodynamics , physics , geology , linguistics , philosophy
Richards equation (RE) of Brooks–Corey soil is invariant under some scaling transformations and can be reduced to ordinary differential equations (ODEs) with scale symmetry analysis. From the reduced ODE, it is convenient to get the solution of RE (mostly numerically). The admissible scaling transformations of RE can transform a given solution to other solutions, by which the explicit relations between wetting front (or its velocity) and boundary moisture and between cumulative infiltration and boundary moisture for horizontal infiltration are deduced. For horizontal infiltration into dry soil with constant boundary moisture, the contour of water distribution curve can be represented by a shape factor R , which can be regarded as a constant for a given soil. Based on the reduced ODE and the parameter R , an explicit approximate solution for horizontal soil water infiltration is proposed, which just relies on R . The shape factor R is related to Brooks–Corey power exponent n and independent of the boundary moisture. With the obtained R – n relations, the relative deviation of the approximate solution can be less than 0.001. The approximate solution keeps high precision in any time range of the infiltration process.