Homogenization of a Reynolds equation describing compressible flow

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Almqvist, Andreas¹  Fabricius, John¹  Wall, Peter¹ 

[1] Lulea Univ Technol, Dept Engn Sci & Math, SE-97187 Lulea, Sweden

关键词: Homogenization;    Multiscale convergence;    Two-scale convergence;    Hydrodynamic lubrication;    Reynolds equation;    Surface roughness;   

DOI  :  10.1016/j.jmaa.2012.02.005

来源: Elsevier

【 摘 要 】

We homogenize a Reynolds equation with rapidly oscillating film thickness function h(epsilon), assuming a constant compressibility 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 L-2 for the unknown density pt.. By adding a small corrector term, convergence is obtained also in the Sobolev norm. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free