An Evolve-Then-Filter Regularized Reduced Order Model

In this paper, we propose a new evolve-then-filter reduced order model (EF-ROM). This is a regularized ROM (Reg-ROM), which aims at the numerical stabilization of 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 new 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 $Re=1000$. 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.

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