  Galerkin-based reduced-order models (G-ROMs) have provided efficient and
accurate approximations of laminar flows. In order to capture the complex
dynamics of the turbulent flows, standard G-ROMs require a relatively large
number of reduced basis functions (on the order of hundreds and even
thousands). Although the resulting G-ROM is still relatively low-dimensional
compared to the full-order model (FOM), its computational cost becomes
prohibitive due to the 3rd-order convection tensor contraction. The tensor
requires storage of $N^3$ entries with a corresponding work of $2N^3$
operations per timestep, which makes such ROMs impossible to use in realistic
applications, such as control of turbulent flows. In this paper, we focus on
the scenario where the G-ROM requires large $N$ values and propose a novel
approach that utilizes the CANDECOMC/PARAFAC decomposition (CPD), a tensor
decomposition technique, to accelerate the G-ROM by approximating the 3rd-order
convection tensor by a sum of $R$ rank-1 tensors. In addition, we show that the
tensor is partially skew-symmetric and derive two conditions for the CP
decomposition for preserving the skew-symmetry. Moreover, we investigate the
G-ROM with the singular value decomposition (SVD). The G-ROM with CP
decomposition is investigated in several flow configurations from 2D periodic
flow to 3D turbulent flows. Our numerical investigation shows CPD-ROM achieves
at least a factor of 10 speedup. Additionally, the skew-symmetry preserving
CPD-ROM is more stable and allows the usage of smaller rank $R$. Moreover, from
the singular value behavior, the advection tensor formed using the $H^1_0$-POD
basis has a low-rank structure, and is preserved even in higher Reynolds
numbers. Furthermore, for a given level of accuracy, the CP decomposition is
more efficient in size and cost than the SVD.
