  The present paper is devoted to the joint motion of two immiscible
incompressible liquids in porous media. The liquids have different densities
and initially separated by a surface of strong discontinuity (free boundary).
We discuss the results of numerical simulations for exact free boundary
problems on the microscopic level for the absolutely rigid solid skeleton and
for the elastic solid skeleton of different geometries. The problems have a
natural small parameter, which is the ratio of average pore size to the size of
the domain in consideration. The formal limits as $\epsilon\searrow 0$ results
homogenized models, which are the Muskat problem in the case of the absolutely
rigid solid skeleton, and the viscoelastic Muskat problem in the case of the
elastic solid skeleton. The last model preserves a free boundary during the
motion, while in the first model instead of the free boundary appears a mushy
region, occupied by a mixture of two fluids.
