EFFECTIVE PRESSURE INTERFACE LAW FOR TRANSPORT PHENOMENA BETWEEN AN UNCONFINED FLUID AND A POROUS MEDIUM USING HOMOGENIZATION ∗
Anna Marciniak‐Czochra, Andro, Mikeli Ć · 2013
Abstract. We present modeling of the incompressible viscous flows in the domain containing unconfined fluid and a porous medium in the case when the flow in the unconfined domain dominates. For such a setting a rigorous derivation of the Beavers–Joseph–Saffman interface condition was undertaken by Jäger and Mikelić [SIAM J. Appl. Math., 60 (2000), pp. 1111–1127] using the homogenization method. So far the interface law for the pressure was conceived and confirmed only numerically. In this article we derive the Beavers and Joseph law for a general body force by estimating the pressure field approximation. Different from the Poiseuille flow case, the velocity approximation is not divergence-free and the precise pressure estimation is essential. This new estimate allows us to rigorously justify the pressure jump condition using the Navier boundary layer, already used to calculate the constant in the law by Beavers and Joseph. Finally, our results confirm that the position of the interface influences the solution only at the order of physical permeability and therefore the choice of this position does not pose problems.