  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.
