Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under-resolved or marginally-resolved simulations of convection-dominated flows. In this paper we investigate the role of numerical stabilization in reduced order models (ROMs) of convection-dominated, marginally-resolved flows. Specifically, we investigate the FOM-ROM consistency, i.e., whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve-filter-relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM-ROM consistency, we consider two ROM strategies: (i) the EFR-ROM, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR-EFRROM, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR-ROM with the EFR-EFRROM in the numerical simulation of a 2D flow past a circular cylinder in the convection-dominated, marginally-resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR-EFRROM is more accurate than the EFR-ROM, which suggests that FOM-ROM consistency is beneficial in convection-dominated, marginally-resolved flows.
翻译:数字稳定通常用于消除(减少)由完全排序模型产生的虚假振动,这些模型一般以溶解不足或略解溶解的对流主导模拟中以平流为主的全序模型(FOMs)为主。在本文件中,我们调查数字稳定在以对流为主、略解流为主的减序模型(ROMs)中的作用。具体地说,我们调查FOM-ROM的一致性,即数字稳定是否对FOM和ROM都有利。作为一个数字稳定战略,我们侧重于以空间过滤为核心的递进-过滤器(EFRM)正规化算法。为了调查FOM-ROM的一致性,我们考虑两种ROM战略:(i) EFR-ROM(ROM) :EFR-ROM(ROM) 稳定在FR水平上使用,而不是ROM(E-FR) 稳定在FR一级使用E的 EFR-ROM(E-RM) 。我们将E-ROM(E-ROM) 的精确流流与E-RM(E-RRM) 模拟的E-RMRMRM(E-RM) 显示的E-C-C-C-C-C-CRMLULO-C-C-C-RM) 的递解解缩算取。