Numerical comparisons of finite element stabilized methods for a 2D vortex dynamics simulation at high Reynolds number

Abstract

In this paper, we consider up-to-date and classical Finite Element (FE) stabilized methods for time-dependent incompressible flows. All studied methods belong to the Variational MultiScale (VMS) framework. So, different realizations of stabilized FE-VMS methods are compared using a high Reynolds number vortex dynamics simulation. In particular, a fully Residual-Based (RB)-VMS method is compared with the classical Streamline-Upwind Petrov–Galerkin (SUPG) method together with grad–div stabilization, a standard one-level Local Projection Stabilization (LPS) method, and a recently proposed LPS method by interpolation. These procedures do not make use of the statistical theory of equilibrium turbulence, and no ad-hoc eddy viscosity modeling is required for all methods. Applications to the simulation of a high Reynolds number flow with vortical structures on relatively coarse grids are showcased, by focusing on a two-dimensional plane mixing-layer flow. Both Inf–Sup Stable (ISS) and Equal Order (EO) H1-conforming FE pairs are explored using a second-order semi-implicit Backward Differentiation Formula (BDF2) in time. Based on the numerical studies conducted, it is concluded that the SUPG method using EO–FE pairs performs best among all methods. Furthermore, there seems to be no reason to extend the SUPG method by the higher order terms of the RB-VMS method.