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arXiv · 2405.12108

An effective advection induced by oscillating microstructure in a diffusion equation

David Wiedemann
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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.

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David Wiedemann. 2024-05-20. An effective advection induced by oscillating microstructure in a diffusion equation. https://arxiv.org/abs/2405.12108

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