Homogenization and low Mach number limit of compressible Navier-Stokes equations in critically perforated domains

Abstract

In this note, we consider the homogenization of the compressible Navier-Stokes equations in a periodically perforated domain in R3. Assuming that the particle size scales like ε3, where ε>0 is their mutual distance, and that the Mach number decreases fast enough, we show that in the limit ε→0, the velocity and density converge to a solution of the incompressible Navier-Stokes equations with Brinkman term. We strongly follow the methods of Höfer, Kowalczyk and Schwarzacher [https://doi.org/10.1142/S0218202521500391], where they proved convergence to Darcy’s law for the particle size scaling like εα with α∈(1,3).