Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir–capillaries interface

In this article the Stokes equations are considered in a domain simulating a capillary bed system. The capillaries are supposed to be thin, parallel and periodic. An asymptotic approximation is constructed. The macroscopic pressure satisfies a Robin interface condition whose coefficients are calculated numerically through a finite element approximation of a boundary layer problem, which is inspired to a domain decomposition technique.