Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers
Hill, A. A. and 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, 466 (2121). pp. 2695-2705. ISSN 1364-5021
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Publisher's URL: http://dx.doi.org/10.1098/rspa.2010.0014
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.
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