Homogenization of degenerate coupled transport processes in porous media with memory terms

TL;DR

This paper develops a homogenization framework for complex coupled transport processes with memory effects in porous media, demonstrating two-scale convergence from meso-scale to upscaled models.

Contribution

It introduces a homogenization approach for degenerate, memory-including coupled transport systems in porous media, extending existing models to account for heterogeneity and memory effects.

Findings

Proves two-scale convergence of solutions as the heterogeneity scale vanishes.

Derives an effective upscaled model capturing memory effects in porous media.

Provides a rigorous mathematical foundation for homogenization in complex porous systems.

Abstract

In this paper we establish a homogenization result for a doubly nonlinear parabolic system arising from the hygro-thermo-chemical processes in porous media taking into account memory phenomena. We present a meso-scale model of the composite (heterogeneous) material where each component is considered as a porous system and the voids of the skeleton are partially saturated with liquid water. It is shown that the solution of the meso-scale problem is two-scale convergent to that of the upscaled problem as the spatial parameter goes to zero.