Homogenization of a Reynolds equation describing compressible flow

We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressibility factor in the pressure–density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term, convergence is obtained also in the Sobolev norm.