Homogenization of the Stokes equation with mixed boundary condition in a porous medium
John Fabricius, Elena Miroshnikova, Peter Wall · Cogent Mathematics · 2017
We homogenize stationary incompressible Stokes flow in a periodic porous medium. The fluid is assumed to satisfy a no-slip condition on the boundary of solid inclusions and a normal stress (traction) condition on the global boundary. Under these assumptions, the homogenized equation becomes the classical Darcy law with a Dirichlet condition for the pressure.