An evolve‐then‐filter regularized reduced order model for convection‐dominated flows. (23rd February 2017) - Wells, D.; Wang, Z.; Xie, X.; Iliescu, T.
Summary: In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM). This is a regularized ROM (Reg‐ROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convection‐dominated flows. We also consider the Leray ROM (L‐ROM). These two Reg‐ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four Reg‐ROM/filter combinations are tested in the numerical simulation of the three‐dimensional flow past a circular cylinder at a Reynolds number R e =1000. Overall, the most accurate Reg‐ROM/filter combination is EF‐ROM‐DF. Furthermore, the spatial filter has a higher impact on the Reg‐ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF‐ROM and L‐ROM. Finally, the CPU times of the four Reg‐ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd. Abstract : In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM), which is a regularized ROM (Reg‐ROM) that increases the numerical stability of ROMs for convection‐dominated flows. This new Reg‐ROM uses two explicit ROM spatial filters (a differential filter and a projection) to smooth (regularize) various terms in the ROMs. The new EF‐ROM produces accurate and efficient numerical approximations of a three‐dimensional flow past a circular cylinder at a Reynolds number Re = 1000.