A Darcy law with memory by homogenisation for evolving microstructure

2024/03/13 by Wiedemann, David, Peter, Malte A. · 2 citations
#35B27 #35R37 #76D07 #76M50 #76S05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.08166

Abstract

We consider the homogenisation of the instationary Stokes equations in a porous medium with an a-priori given evolving microstructure. In order to pass to the homogenisation limit, we transform the Stokes equations to a domain with a fixed periodic microstructure. The homogenisation result is a Darcy-type equation with memory term and has the form of an integro-differential equation. The evolving microstructure leads to a time and space dependent permeability coefficient and the local change of the porosity causes an additional source term for the pressure.

Cited by

• Effective transmission through an interface with evolving microstructure
• Effective permeabilities for flow through anisotropic microscopic geometries

Related

• Homogenisation of the Stokes equations for evolving microstructure
• Rigorous derivation of an effective model for coupled Stokes advection, reaction and diffusion with freely evolving microstructure
• Darcy's Law for Porous Media with Multiple Microstructures
• Homogenization of the Stokes system in a non-periodically perforated domain
• Homogenization of some evolutionary non-Newtonian flows in porous media