In this paper, we propose a novel ROM stabilization strategy for under-resolved convection-dominated flows, the approximate deconvolution Leray ROM (ADL-ROM). The new ADL-ROM introduces AD as a new means to increase the accuracy of the classical Leray ROM (L-ROM) without degrading its numerical stability. We also introduce two new AD ROM strategies: the Tikhonov and van Cittert methods. Our numerical investigation for convection-dominated systems shows that, when the filter radius is relatively large, the new ADL-ROM is more accurate than the standard L-ROM. Furthermore, the new ADL-ROM is less sensitive with respect to model parameters than L-ROM.

翻译：本文针对未充分解析的对流主导流动，提出一种新颖的ROM稳定化策略——近似反卷积Leray降阶模型（ADL-ROM）。该新型ADL-ROM引入近似反卷积（AD）作为新手段，在不降低数值稳定性的前提下提升经典Leray降阶模型（L-ROM）的精度。同时提出两种新型AD-ROM策略：Tikhonov方法与van Cittert方法。对对流主导系统的数值研究表明：当滤波半径较大时，新型ADL-ROM比标准L-ROM具有更高精度；此外，新型ADL-ROM对模型参数的敏感性低于L-ROM。