Homogenization of the time discretized compressible Navier–Stokes system

Abstract

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