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In this paper, we consider up-to-date and classical Finite Element (FE)stabilized methods for time-dependent incompressible flows. All studied methodsbelong to the Variational MultiScale (VMS) framework. So, differentrealizations of stabilized FE-VMS methods are compared in high Reynolds numbersvortex dynamics simulations. In particular, a fully Residual-Based (RB)-VMSmethod is compared with the classical Streamline-Upwind Petrov--Galerkin (SUPG)method together with grad-div stabilization, a standard one-level LocalProjection Stabilization (LPS) method, and a recently proposed LPS method byinterpolation. These procedures do not make use of the statistical theory ofequilibrium turbulence, and no ad-hoc eddy viscosity modeling is required forall methods. Applications to the simulations of high Reynolds numbers flowswith vortical structures on relatively coarse grids are showcased, by focusingon two-dimensional plane mixing-layer flows. Both Inf-Sup Stable (ISS) andEqual Order (EO) FE pairs are explored, using a second-order semi-implicitBackward Differentiation Formula (BDF2) in time. Based on the numericalstudies, it is concluded that the SUPG method using both ISS and EO FE pairsperforms best among all methods. Furthermore, there seems to be no reason toextend SUPG method by the higher order terms of the RB-VMS method.

Numerical comparisons of finite element stabilized methods for high Reynolds numbers vortex dynamics simulations