Effect models for the stationary Navier–Stokes fluid in a porous medium with different scales

Abstract

In this paper, we investigate an incompressible flow through a thin corrugated domain fill with fluid saturated porous medium. The porous medium flow is governed by Navier–Stokes model. The thickness of the domain is assumed to be aɛ and the solid part is supposed to be periodical cylinders of size ɛ. We rigorously derive different asymptotic models by comparing the relation between ɛ and aɛ. To prove the main results, we employ the homogenization technique based on the generalized Poincaré inequality.