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Convergence to the Reynolds approximation with a double effect of roughness

Authors
  • Choquet, Catherine
  • Chupin, Laurent
  • Gisclon, Marguerite
Type
Preprint
Publication Date
Feb 17, 2010
Submission Date
Feb 17, 2010
Source
arXiv
License
Yellow
External links

Abstract

We prove that the lubrication approximation is perturbed by a non-regular roughness of the boundary. We show how the flow may be accelerated using adequate rugosity profiles on the bottom. We explicit the possible effects of some abrupt changes in the profile. The limit system is mathematically justified through a variant of the notion of two-scale convergence. Finally, we present some numerical results, illustrating the limit system in the three-dimensional case.

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