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Direct numerical simulations (DNS) indicate that at large values of theRayleigh number ($Ra$) convection in porous media self-organizes intonarrowly-spaced columnar flows, with more complex spatiotemporal features beingconfined to boundary layers near the top and bottom walls. In thisinvestigation of high-$Ra$ porous media convection in a minimal flow unit, tworeduced modeling strategies are proposed that exploit these specific flowcharacteristics. Both approaches utilize the idea of decomposition since theflow exhibits different dynamics in different regions of the domain:small-scale cellular motions generally are localized within the thermal andvorticity boundary layers near the upper and lower walls, while in theinterior, the flow exhibits persistent large-scale structures and only a fewlow (horizontal) wavenumber Fourier modes are active. Accordingly, in the firststrategy, the domain is decomposed into two near-wall regions and one interiorregion. Our results confirm that suppressing the interior high-wavenumber modeshas negligible impact on the essential structural features and transportproperties of the flow. In the second strategy, a hybrid reduced model isconstructed by using Galerkin projection onto a fully \emph{a priori}eigenbasis drawn from energy stability and upper bound theory, therebyextending the model reduction strategy developed by Chini \emph{et al.}(\emph{Physica~D}, vol. 240, 2011, pp. 241--248) to large $Ra$. The resultsindicate that the near-wall upper-bound eigenmodes can economically representthe small-scale rolls within the exquisitely-thin thermal boundary layers.Relative to DNS, the hybrid algorithm enables over an order-of-magnitudeincrease in computational efficiency with only a modest loss of accuracy.

Reduced modeling of porous media convection in a minimal flow unit at large Rayleigh number