Convergence to the Reynolds approximation with a double effect of roughness

Details Convergence to the Reynolds approximation with a double effect of roughness Convergence to the Reynolds approximation with a double effect of roughness

2010-02-17

arxiv.org/abs/1002.3215v1

Mathematics

Analysis of PDEs

Scientific paper

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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