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

摘要

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 FEVMS 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) H-1-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. (C) 2019 Elsevier B.V. All rights reserved.