Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers
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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.
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
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
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