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Theory and numerical analysis of moving boundary problems in the hydrodynamics of porous media
Author(s) -
Nakano Yoshisuke
Publication year - 1978
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/wr014i001p00125
Subject(s) - porous medium , infinitesimal , flow (mathematics) , boundary (topology) , mathematics , boundary value problem , mechanics , simplicity , wetting , finite difference , finite difference method , porosity , calculus (dental) , mathematical analysis , geotechnical engineering , geometry , geology , physics , thermodynamics , medicine , dentistry , quantum mechanics
The exact mathematical descriptions of a boundary between unsaturated flow and saturated flow as well as a wetting front are obtained. A new concept for numerical analysis of flow in a partly unsaturated and partly saturated porous medium is introduced. A boundary of infinitesimal width intersecting the unsaturated and saturated parts is substituted by an artificial transitional zone of finite width for computational simplicity. The concept is proved to be theoretically justifiable. The feasibility of the concept is demonstrated as it is applied to a two‐dimensional finite difference solution of a special problem of column drainage, for which an analytical solution is obtained.