Upscaling of a double porosity problem with jumps in thin porous media

ABSTRACT

We study the homogenization of a double porosity diffusion problem in a thin highly heterogeneous composite medium formed by two materials separated by an imperfect interface, where the solution and its flux exhibit jumps. By applying homogenization techniques specific to the thin periodic domain under study, one derives the limit problem.

Keywords:

• Thin domain
• porous medium
• imperfect interface
• asymptotic methods

AMS subject classifications:

• 76A20
• 76S05
• 74A50
• 76M45

Acknowledgements

This paper was completed during the visit of the second author at IECL,whose warm hospitality is gratefully acknowledged. Both authors are grateful to the anonymous referee for her/his valuable comments and suggestions, which improved the content and the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).