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A framework for computing effective boundary conditions at the interface between free fluid and a porous medium
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0003-3094-0848
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-8209-1449
2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 812, p. 866-889Article in journal (Refereed) Published
Abstract [en]

Interfacial boundary conditions determined from empirical or ad hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using a multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (J. Fluid Mech., vol. 30 (01), 1967, pp. 197-207). The components of the tensors determining the effective slip velocity at the interface are obtained by solving a set of Stokes equations in a small computational domain near the interface containing both free flow and porous medium. Using the lid-driven cavity flow with a porous bed, we demonstrate that the derived boundary condition is accurate and robust by comparing an effective model to direct numerical simulations. Finally, we provide an open source code that solves the microscale problems and computes the velocity boundary condition without free parameters over any porous bed.

Place, publisher, year, edition, pages
Cambridge University Press, 2017. Vol. 812, p. 866-889
Keywords [en]
Computational methods, Mathematical foundations, Porous media
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-200998DOI: 10.1017/jfm.2016.838ISI: 000392712400039Scopus ID: 2-s2.0-85008391603OAI: oai:DiVA.org:kth-200998DiVA, id: diva2:1072205
Note

QC 20170207

Available from: 2017-02-07 Created: 2017-02-07 Last updated: 2017-11-29Bibliographically approved

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