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On the effective equations of a viscous incompressible fluid flow through a filter of finite thickness
Author(s) -
Jäger Willi,
Mikelić Andro
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199809/10)51:9/10<1073::aid-cpa6>3.0.co;2-a
Subject(s) - mathematics , compressibility , filter (signal processing) , pressure drop , convergence (economics) , mathematical analysis , boundary (topology) , flow (mathematics) , incompressible flow , mechanics , constant (computer programming) , axial symmetry , viscous liquid , boundary value problem , geometry , physics , computer science , economics , computer vision , programming language , economic growth
Abstract We consider an incompressible and nonstationary fluid flow, governed by a given pressure drop, in a domain that contains a filter of finite thickness. The filter consists of a big number of tiny, axially symmetric tubes with nonconstant sections. We prove the global existence for the ε‐problem and find out the effective behavior of the velocity and the pressure fields. The effective velocity in the filter part is a constant vector in the axial direction, and the effective pressure obeys the so‐called fourth‐power law. In the other parts of Ω, the effective flow is determined through the stabilization constants of boundary layers. We prove Saint‐Venant's principle and use those boundary layers to prove the convergence as ε → 0. © 1998 John Wiley & Sons, Inc.