  Motivated by casting of fresh concrete in reinforced concrete structures, we
introduce a numerical model of a steady-state non-Newtonian fluid flow through
a porous domain. Our approach combines homogenization techniques to represent
the reinforced domain by the Darcy law with an interface coupling of the Stokes
and Darcy flows through the Beavers-Joseph-Saffman conditions. The ensuing
two-scale problem is solved by the Finite Element Method with consistent
linearization and the results obtained from the homogenization approach are
verified against fully resolved direct numerical simulations.
