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arXiv · 2403.08166

A Darcy law with memory by homogenisation for evolving microstructure

David Wiedemann·Malte A. Peter
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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.

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David Wiedemann, Malte A. Peter. 2024-03-13. A Darcy law with memory by homogenisation for evolving microstructure. https://arxiv.org/abs/2403.08166

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