The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface

The asymptotic analysis of a Darcy-Stokes system modeling the fluid exchange between a narrow channel (Stokes) and a porous medium (Darcy) coupled through a \( C^{2} \) curved interface, is presented. The channel is a cylindrical domain between the interface (\( \Gamma \)) and a parallel translation...

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Bibliographic Details
Published in:arXiv.org 2019-02
Main Author: Morales, Fernando A
Format: Article
Language:English
Subjects:
Asymptotic properties
Computational fluid dynamics
Porous media
Online Access:Get full text
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Summary:The asymptotic analysis of a Darcy-Stokes system modeling the fluid exchange between a narrow channel (Stokes) and a porous medium (Darcy) coupled through a \( C^{2} \) curved interface, is presented. The channel is a cylindrical domain between the interface (\( \Gamma \)) and a parallel translation of it (\( \Gamma + \epsilon \, \boldsymbol{\widehat{e}}_{N} \)). The introduction of a change variable to fix the domain's geometry and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find a Darcy-Brinkman lower dimensional coupled system as the limiting form, when the width of the channel tends to zero (\( \epsilon \rightarrow 0 \)).
ISSN:2331-8422
DOI:10.48550/arxiv.1902.08642