Reduced-Dimensional Models of Porous-Medium Convection.

Porous-medium Convection;Dynamical Systems;Reduced Modeling;Mathematics;Physics;Science;Physics

Dianati Maleki, NavidSander, Leonard M. ;

University of Michigan

关键词: Porous-medium Convection;    Dynamical Systems;    Reduced Modeling;    Mathematics;    Physics;    Science;    Physics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/97981/navid_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We study the problem of convection in a fluid-saturated porous medium in two di-mensions. Using resolved direct numerical simulations, we show that in the turbulentregime, the width of the smallest periodic box capable of sustaining a convective cellwith the ;;correct” large-aspect ratio vertical heat transport closely matches the averagewidth of the minimal flow unit, i.e., the convective cell naturally developing in a largebox. This suggests that the minimal flow unit is indeed the smallest autonomous dy-namical unit of the flow. Next, we develop a Galerkin spectral method using an adaptedbasis derived from upper-bound theory and compare its performance with that of theFourier-Galerkin method. We show that the adapted method is superior at severetruncations, but not discernibly advantageous asymptotically.