Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection

• DOI: 10.1016/j.physleta.2013.09.009
• Publication Date: 2013-09-12T21:33:18Z
• Authors: Baole Wen; Gregory P. Chini; Navid Dianati; Charles R. Doering
• Keywords: 0103 physical sciences; 01 natural sciences

Abstract Direct numerical simulation (DNS) has shown that Rayleigh–Benard convection in a fluid-saturated porous medium self-organizes into narrowly spaced plumes at (ostensibly) asymptotically high values of the Rayleigh number Ra. In this Letter a combination of DNS and upper bound theory is used to investigate the dependence of the Nusselt number Nu on the domain aspect ratio L at large Ra. A novel algorithm is introduced to solve the optimization problems arising from the upper bound analysis, allowing for the best available bounds to be extended up to Ra ≈ 2.65 × 10 4 . The dependence of the bounds on L ( Ra ) is explored and a “minimal flow unit” is identified.