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NUMERICAL SOLUTION OF TRANSIENT, FREE SURFACE PROBLEMS IN POROUS MEDIA
Author(s) -
VOLLER V. R.,
PENG S.,
CHEN Y. F.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960915)39:17<2889::aid-nme980>3.0.co;2-w
Subject(s) - discretization , porous medium , grid , finite volume method , focus (optics) , regular grid , control volume , mathematics , transient (computer programming) , surface (topology) , numerical analysis , mechanics , mathematical analysis , mathematical optimization , porosity , computer science , geometry , engineering , physics , optics , operating system , geotechnical engineering
The focus of this paper is the development of numerical schemes for tracking the moving fluid surface during the filling of a porous medium (e.g., polymer injection into a porous mold cavity). Performing a mass balance calculation on an arbitrarily deforming control volume, leads to a general governing filling equation. From this equation, a general, fully time implicit, numerical scheme based on a finite volume space discretization is derived. Two numerical schemes are developed: (1) a fully deforming grid scheme, which explicitly tracks the location of the filling front, and (2) a fixed grid scheme, that employs an auxiliary variable to locate the front. The validity of the two schemes is demonstrated by solving a variety of one‐ and two‐dimensional problems; both approaches provide predictions with similar accuracy and agree well with available analytical solutions.