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Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

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HillCarr2.pdf (153.7Kb)
Date
09/2010
Author
Hill, A A
Carr, Magda
Keywords
Superposed porous-fluid convection
One-domain approach
Energy method
QA Mathematics
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Abstract
Studies of the nonlinear stability of fluid/porous systems have been developed very recently. A two-domain modelling approach has been adopted in previous works, but was restricted to specific configurations. The extension to the more general case of a Navier–Stokes modelled fluid over a porous material was not achieved for the two-domain approach owing to the difficulties associated with handling the interfacial boundary conditions. This paper addresses this issue by adopting a one-domain approach, where the governing equations for both regions are combined into a unique set of equations that are valid for the entire domain. It is shown that the nonlinear stability bound, in the one-domain approach, is very sharp and hence excludes the possibility of subcritical instabilities. Moreover, the one-domain approach is compared with an equivalent two-domain approach, and excellent agreement is found between the two.
Citation
Hill , A A & Carr , M 2010 , ' Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers ' , Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences , vol. 466 , no. 2121 , pp. 2695-2705 . https://doi.org/10.1098/rspa.2010.0014
Publication
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Status
Peer reviewed
DOI
https://doi.org/10.1098/rspa.2010.0014
ISSN
1364-5021
Type
Journal article
Rights
This is the author's version of this article. The published version © 2010 The Royal Society is available from http://rspa.royalsocietypublishing.org
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  • University of St Andrews Research
URL
http://www.scopus.com/inward/record.url?scp=77957205298&partnerID=8YFLogxK
URI
http://hdl.handle.net/10023/3398

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