A Darcy law with memory by homogenisation for evolving microstructure
Analysis of PDEs
2024-03-14 v1
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.
Cite
@article{arxiv.2403.08166,
title = {A Darcy law with memory by homogenisation for evolving microstructure},
author = {David Wiedemann and Malte A. Peter},
journal= {arXiv preprint arXiv:2403.08166},
year = {2024}
}
Comments
34 pages