Unfolding homogenization in doubly periodic media and applications

Abstract

We define a reiterated unfolding operator for a doubly periodic domain presenting two periodicity scales. Then we show how to apply it to the homogenization of both linear and nonlinear problems. The main novelty is that this method allows the use of test functions with one scale of periodicity only and it considerably simplifies the proofs of the convergence results. We illustrate this new approach on a Poisson problem with Dirichlet boundary conditions and on the flow of a power law fluid in a doubly periodic porous medium.

Keywords:

• Homogenization
• flows in porous media

AMS Subject Classifications:

• 35B27
• 76S05

Acknowledgements

The first author thanks Professor Alain Damlamian for the very interesting and useful discussions.

Notes

No potential conflict of interest was reported by the authors.