Convergence to the Reynolds approximation with a double effect of roughness
Analysis of PDEs
2010-02-18 v1
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.
Keywords
Cite
@article{arxiv.1002.3215,
title = {Convergence to the Reynolds approximation with a double effect of roughness},
author = {Catherine Choquet and Laurent Chupin and Marguerite Gisclon},
journal= {arXiv preprint arXiv:1002.3215},
year = {2010}
}