Reduced-Dimensional Models of Porous-Medium Convection.

[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.

[发布机构] University of Michigan

[效力级别] Dynamical Systems

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