Colloquium - 4/08, 3:00PM, Duncan Hall 1064

Andro Mikelic

Department of Mathematics
University of Lyon 1 - Camille Jordan Institute

"Modeling Effective Pressure Interface Law Between a Free Fluid and a Porous Medium"

In this talk we present rigorous justification of the interface laws describing contact between the flow in an unconfined fluid and a porous bed. The velocity of the free fluid dominates the filtration velocity, but the pressures are of the same order. Main results are the following:

1. We confirm Saffman's form of the Beavers and Joseph law in a new, more general, setting.
2. We show that a perturbation of the interface position, which is an artificial mathematical boundary, of the order O(epsilon) implies a perturbation in the solution of order O(epsilon²). Consequently, there is a freedom in fixing position of the interface. It influences the result only at the next order of the asymptotic expansion.
3. We obtain a uniform bound on the pressure approximation. Furthermore, we prove that there is a jump of the effective pressure on the interface and that it is proportional to the free fluid shear at the interface.
4. We show an independent numerical confirmation of the pressure jump law and of the Beavers-Josph slip law by a direct simulation of the Stokes flow in the porous bed and in the adjacent domain.