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A stabilized mixed finite element method for Darcy–Stokes flow
Author(s) -
Masud Arif
Publication year - 2007
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1508
Subject(s) - finite element method , mathematics , stokes flow , mathematical analysis , interpolation (computer graphics) , flow (mathematics) , tensor (intrinsic definition) , darcy's law , galerkin method , compressibility , navier–stokes equations , porous medium , mechanics , classical mechanics , geometry , physics , geology , geotechnical engineering , porosity , motion (physics) , thermodynamics
This paper presents a new stabilized finite element method for the Darcy–Stokes equations also known as the Brinkman model of lubrication theory. These equations also govern the flow of incompressible viscous fluids through permeable media. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. Modelling of the unresolved scales corrects the lack of stability of the standard Galerkin formulation for the Darcy–Stokes equations. A significant feature of the present method is that the structure of the stabilization tensor τ appears naturally via the solution of the fine‐scale problem. The issue of arbitrary combinations of pressure–velocity interpolation functions is addressed, and equal‐order combinations of C ° interpolations are shown to be stable and convergent. Copyright © 2007 John Wiley & Sons, Ltd.