On the effective equations of a viscous incompressible fluid flow through a filter of finite thickness

✍ Scribed by Willi Jäger; Andro Mikelić

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 577 KB
• Volume: 51
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/(sici)1097-0312(199809/10)51:9/10<1073::aid-cpa6>3.0.co;2-a

✦ Synopsis

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 εproblem 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.