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On the incompatibility of Richards' equation and finger‐like infiltration in unsaturated homogeneous porous media
Author(s) -
Fürst Tomáš,
Vodák Rostislav,
Šír Miloslav,
Bíl Michal
Publication year - 2009
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2008wr007062
Subject(s) - homogeneous , porous medium , richards equation , hydraulic conductivity , monotone polygon , mathematics , infiltration (hvac) , boundary value problem , vadose zone , porosity , flow (mathematics) , calculus (dental) , mathematical analysis , geotechnical engineering , materials science , geometry , geology , composite material , soil science , water content , soil water , medicine , dentistry , combinatorics , groundwater
It is demonstrated by means of a mathematical proof that Richards' equation, in principle, cannot admit finger‐like solutions for three‐dimensional homogeneous unsaturated porous media flow, subject to monotone boundary conditions. This is demonstrated for any reasonable type of homogeneous porous material; the result is not dependent on any particular form of the hydraulic conductivity or the retention curve. Moreover, it is explained why hysteresis of the retention curve does not play any role in the proof. Consequently, the proof is true for any type of hysteretic behavior of the retention curve. An alternative approach to finger flow modeling is discussed which uses the ideas of cellular automata.