标题： 大瑞利数下最小流动单元中多孔介质对流的简化建模 显示英文标题

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

摘要： 直接数值模拟（DNS）表明，当瑞利数（$Ra$）较大时，多孔介质中的对流自组织成狭窄间距的柱状流动，更复杂的时空特征被限制在顶部和底部壁附近的边界层内。 在本研究中，针对最小流动单元中的高$Ra$多孔介质对流，提出了两种简化的建模策略，这些策略利用了特定的流动特征。 这两种方法都利用了分解的思想，因为流动在域的不同区域表现出不同的动力学特性：小尺度的细胞运动通常局限于靠近上下壁的热边界层和涡度边界层，而在内部，流动表现出持续的大尺度结构，只有少数低（水平）波数傅里叶模式是活跃的。 因此，在第一种策略中，域被分解为两个近壁区域和一个内部区域。 我们的结果证实，抑制内部高波数模式对流动的基本结构特征和传输性质几乎没有影响。 在第二种策略中，通过将伽辽金投影应用于从能量稳定性与上界理论中提取的完全\emph{事前}特征基，构建了一个混合简化模型，从而将由 Chini\emph{等.}开发的模型简化策略（\emph{物理学期刊}，第 240 卷，2011 年，第 241--248 页）扩展到大$Ra$。 结果表明，近壁上界特征模式可以经济地表示极其薄的热边界层内的小尺度滚流。 与 DNS 相比，该混合算法在仅略有精度损失的情况下，计算效率提高了数量级。 显示英文摘要

摘要： Direct numerical simulations (DNS) indicate that at large values of the Rayleigh number ($Ra$) convection in porous media self-organizes into narrowly-spaced columnar flows, with more complex spatiotemporal features being confined to boundary layers near the top and bottom walls. In this investigation of high-$Ra$ porous media convection in a minimal flow unit, two reduced modeling strategies are proposed that exploit these specific flow characteristics. Both approaches utilize the idea of decomposition since the flow exhibits different dynamics in different regions of the domain: small-scale cellular motions generally are localized within the thermal and vorticity boundary layers near the upper and lower walls, while in the interior, the flow exhibits persistent large-scale structures and only a few low (horizontal) wavenumber Fourier modes are active. Accordingly, in the first strategy, the domain is decomposed into two near-wall regions and one interior region. Our results confirm that suppressing the interior high-wavenumber modes has negligible impact on the essential structural features and transport properties of the flow. In the second strategy, a hybrid reduced model is constructed by using Galerkin projection onto a fully \emph{a priori} eigenbasis drawn from energy stability and upper bound theory, thereby extending the model reduction strategy developed by Chini \emph{et al.} (\emph{Physica~D}, vol. 240, 2011, pp. 241--248) to large $Ra$. The results indicate that the near-wall upper-bound eigenmodes can economically represent the small-scale rolls within the exquisitely-thin thermal boundary layers. Relative to DNS, the hybrid algorithm enables over an order-of-magnitude increase in computational efficiency with only a modest loss of accuracy.