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Scaling of water flow through porous media and soils
Author(s) -
Roth K.
Publication year - 2008
Publication title -
european journal of soil science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.244
H-Index - 111
eISSN - 1365-2389
pISSN - 1351-0754
DOI - 10.1111/j.1365-2389.2007.00986.x
Subject(s) - scaling , richards equation , porous medium , discretization , flow (mathematics) , darcy's law , infiltration (hvac) , soil water , water flow , scale (ratio) , mechanics , mathematics , permeability (electromagnetism) , porosity , geotechnical engineering , calculus (dental) , geology , soil science , physics , thermodynamics , geometry , mathematical analysis , chemistry , biochemistry , quantum mechanics , membrane , medicine , dentistry
Summary Scaling of fluid flow in general is outlined and contrasted to the scaling of water flow in porous media. It is then applied to deduce Darcy’s law, thereby demonstrating that stationarity of the flow field at the scale of the representative elementary volume (REV) is a critical prerequisite. The focus is on the implications of the requirement of stationarity, or local equilibrium, in particular on the validity of the Richards equation for the description of water movement through soils. Failure to satisfy this essential requirement may occur at the scale of the REV or, particularly in numerical simulations, at the scale of the model discretization. The latter can be alleviated by allocation of more computational resources and by working on a finer‐grained representation. In contrast, the former is fundamental and leads to an irrevocable failure of the Richards equation as is observed with infiltration instabilities that lead to fingered flow.