Girelli, A., Giantesio, G., Musesti, A. and Penta, R. (2024) Multiscale homogenisation for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymph node. Royal Society Open Science, 11(7), 231983. (doi: 10.1098/rsos.231983) (PMID:39021765) (PMCID:PMC11253036)
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Abstract
We study the coupling between time-dependent Darcy–Brinkman and the Darcy equations at the microscale subjected to inhomogeneous body forces and initial conditions to describe a double porosity problem. We derive the homogenized governing equations for this problem using the asymptotic homogenization technique, and as macroscopic results, we obtain a coupling between two Darcy equations, one of which with memory effects, with mass exchange between phases. The memory effects are a consequence of considering the time dependence in the Darcy–Brinkman equation, and they allow us to study in more detail the role of time in the problem under consideration. After the formulation of the model, we solve it in a simplified setting and we use it to describe the movement of fluid within a vascularized lymph node.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Penta, Dr Raimondo |
Authors: | Girelli, A., Giantesio, G., Musesti, A., and Penta, R. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Royal Society Open Science |
Publisher: | The Royal Society |
ISSN: | 2054-5703 |
ISSN (Online): | 2054-5703 |
Published Online: | 17 July 2024 |
Copyright Holders: | Copyright © 2024 The Authors |
First Published: | First published in Royal Society Open Science 11(7):231983 |
Publisher Policy: | Reproduced under a Creative Commons licence |
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