Homogenization of 2D Cahn-Hilliard-Navier-Stokes system

TL;DR

This paper performs asymptotic analysis of the 2D Cahn-Hilliard-Navier-Stokes system with microstructures, deriving a homogenized limit model using sigma-convergence beyond periodic settings.

Contribution

It extends homogenization techniques to non-periodic microstructures in the coupled Cahn-Hilliard-Navier-Stokes system using sigma-convergence.

Findings

Derived the limit model equivalent to the heterogeneous system.

Extended homogenization beyond periodic microstructures.

Applied sigma-convergence for the asymptotic analysis.

Abstract

In the current work, we are performing the asymptotic analysis, beyond the periodic setting, of the Cahn-Hilliard-Navier-Stokes system. Under the general deterministic distribution assumption on the microstructures in the domain, we find the limit model equivalent to the heterogeneous one. To this end, we use the sigma-convergence concept which is suitable for the passage to the limit.