An effective advection induced by oscillating microstructure in a diffusion equation
Analysis of PDEs
2024-05-21 v1
Abstract
We consider the homogenisation of a diffusion equation in a porous medium. The microstructure is time-dependent and oscillating on a small time scale. This oscillation causes a novel advection in the homogenised equations. Allowing for a locally varying geometry, the oscillating microstructure demonstrates the ability to generate arbitrary and locally varying advection velocity fields.
Cite
@article{arxiv.2405.12108,
title = {An effective advection induced by oscillating microstructure in a diffusion equation},
author = {David Wiedemann},
journal= {arXiv preprint arXiv:2405.12108},
year = {2024}
}
Comments
33 pages, 2 figures