The evolve-filter (EF) model is a filter-based numerical stabilization for under-resolved convection-dominated flows. EF is a simple, modular, and effective strategy for both full-order models (FOMs) and reduced-order models (ROMs). It is well-known, however, that when the filter radius is too large, EF can be overdiffusive and yield inaccurate results. To alleviate this, EF is usually supplemented with a relaxation step. The relaxation parameter, however, is very sensitive with respect to the model parameters. In this paper, we propose a novel strategy to alleviate the EF overdiffusivity for a large filter radius. Specifically, we leverage the variational multiscale (VMS) framework to separate the large resolved scales from the small resolved scales in the evolved velocity, and we use the filtered small scales to correct the large scales. Furthermore, in the new VMS-EF strategy, we use two different ways to decompose the evolved velocity: the VMS Evolve-Filter-Filter-Correct (VMS-EFFC) and the VMS Evolve-Postprocess-Filter-Correct (VMS-EPFC) algorithms. The new VMS-based algorithms yield significantly more accurate results than the standard EF in both the FOM and the ROM simulations of a flow past a cylinder at Reynolds number Re = 1000.

翻译：演化滤波（EF）模型是一种基于滤波器的数值稳定化方法，适用于欠解析的主导对流流动。EF是一种简单、模块化且有效的策略，适用于全阶模型（FOMs）和降阶模型（ROMs）。然而，众所周知，当滤波半径过大时，EF可能过度扩散并导致不准确的结果。为缓解此问题，EF通常辅以松弛步骤。但松弛参数对模型参数非常敏感。本文提出一种新颖策略，以减轻大滤波半径下EF的过度扩散性。具体而言，我们利用变分多尺度（VMS）框架将演化速度中的大解析尺度与小解析尺度分离，并使用滤波后的小尺度来修正大尺度。此外，在新提出的VMS-EF策略中，我们采用两种不同的方式来分解演化速度：VMS演化-滤波-滤波-修正（VMS-EFFC）算法和VMS演化-后处理-滤波-修正（VMS-EPFC）算法。在雷诺数Re = 1000的圆柱绕流FOM和ROM模拟中，新的基于VMS的算法相比标准EF产生了显著更准确的结果。