Homogenization of the time discretized compressible Navier–Stokes system

This paper is concerned with the homogenization of the time discretized compressible Navier–Stokes system in a periodic porous medium (of period εε) with Dirichlet boundary conditions in two or three dimensions. To this end, we generalized the Poincaré inequality in the porous medium. We apply our results to this model and rigorously derive the so called ‘porous medium equation’ as εε, the pore size tends to zero.