Boundary Layer Associated with the DarcyBrinkmanBoussinesq Model for Convection in Porous Media
We study the asymptotic behavior of the infinite DarcyPrandtl number DarcyBrinkmanBoussinesq system for convection in porous media at a small BrinkmanDarcy number. the existence of a boundary layer with thickness proportional to the square root of the BrinkmanDarcy number for the velocity field is established in both the L∞(H1) norm (in 2 and 3 d) and the L∞(L∞) norm (in 2d). This improves in several respects an earlier result of Payne and Straughan (1998)  where the vanishing BrinkmanDarcy number limit is studied without resolving the boundary layer. © 2010 Elsevier B.V. All rights reserved.
J. P. Kelliher et al., "Boundary Layer Associated with the DarcyBrinkmanBoussinesq Model for Convection in Porous Media," Physica D: Nonlinear Phenomena, vol. 240, no. 7, pp. 619 - 628, Elsevier, Mar 2011.
The definitive version is available at https://doi.org/10.1016/j.physd.2010.11.012
Mathematics and Statistics
Keywords and Phrases
Boundary Layer; BrinkmanDarcy Number; Corrector; Infinite Darcy Prandtl Number DarcyBrinkmanBoussinesq System; Infinite DarcyPrandtl Number DarcyBoussinesq System
International Standard Serial Number (ISSN)
Article - Journal
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15 Mar 2011
National Science Foundation, Grant 0906440