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Homogenization of a Reynolds equation describing compressible flow
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.ORCID iD: 0000-0001-7029-1112
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-1993-8229
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2012 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, no 2, p. 456-471Article in journal (Refereed) Published
Abstract [en]

We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressiblity factor in the pressure-density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term we also obtain strong convergence in the Sobolev norm.

Place, publisher, year, edition, pages
2012. Vol. 390, no 2, p. 456-471
National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
Research subject
Machine Elements; Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-5148DOI: 10.1016/j.jmaa.2012.02.005ISI: 000301027900003Scopus ID: 2-s2.0-84857237758Local ID: 32d5e594-d1fa-4941-965e-2e563f56dc4aOAI: oai:DiVA.org:ltu-5148DiVA, id: diva2:978022
Note
Validerad; 2012; 20120210 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Almqvist, AndreasFabricius, JohnWall, Peter

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  • apa
  • harvard1
  • ieee
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  • de-DE
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  • en-US
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