Rigorous justification of the effective boundary condition on a porous wall via homogenization

Viscous flow through a reservoir with porous boundary is studied via asymptotic analysis and homogenization. Under the assumption of periodicity of the pores, the effective boundary condition is derived and rigorously justified. The velocity on the boundary satisfies a version of the Darcy law. The Darcy law for tangential component can also be seen as the Beavers-Joseph law.

Automated summary

The study focuses on viscous flow through a reservoir with a porous boundary using asymptotic analysis and homogenization. By assuming periodicity of the pores, an effective boundary condition is derived and rigorously justified. The velocity on the boundary follows a version of the Darcy law, which can also be interpreted as the Beavers-Joseph law for the tangential component.