Effective pressure interface law for transport phenomena between an   unconfined fluid and a porous medium using homogenization
  We present modeling of the incompressible viscous flows in the domain containing an unconfined fluid and a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interface condition was undertaken by J\"ager and Mikeli\'c [SIAM J. Appl. Math. \rm 60 (2000), p. 1111-1127] using the homogenization method. So far the interface law for the pressure was conceived and confirmed only numerically. In this article we justify rigorously the pressure jump condition using the corresponding boundary layer. 
Anna Marciniak-Czochra and Andro Mikelic
math.AP physics.flu-dyn physics.geo-ph