Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

Abstract

In this work we study the performance of some variational multiscale models (VMS) in the large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by different subgrid scale approximations which include either static or dynamic subscales, linear or nonlinear multiscale splitting and different choices of the subscale space. After a brief review of these models, we discuss some implementation aspects particularly relevant to the simulation of turbulent flows, namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used. We analyze the energy conservation (and numerical dissipation) of the alternative VMS formulations, which is numerically evaluated. In the numerical study, we have considered three well known problems: the decay of homogeneous isotropic turbulence, the Taylor-Green vortex problem and the turbulent flow in a channel. We compare the results obtained using the different VMS models and against a classical LES scheme based on filtering and the Smagorinsky closure. Altogether, our results show the tremendous potential of VMS for the numerical simulation of turbulence. Further, we study the sensitivity of VMS to the algorithmic constants and analyze the behavior in the small time step limit. We have also carried out a computational cost comparison of the different formulations. Out of these results, we can state that the numerical results obtained with the different VMS formulations (as far as they converge) are quite similar. However, some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different. The dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness.

A FIC-based stabilized finite element formulation for turbulent flows

“…In particular, this problem has been simulated using a variety of stabilized formulations, both using classical finite elements [4,5,6,16] and isogeometric elements [14,13]. This Reynolds number is very convenient because it allows us to use a mesh with enough resolution close to the wall while keeping the computational cost under control.…”

“…This approach to turbulence modeling has been tested numerically in multiple studies (e.g. [13,14,15,16]). …”

Variational Multiscale based dissipation models for the estimation of atmospheric seeing

“…Due to this, num can be understood as the dissipation caused by the turbulent effects of the flow (see [19,24]). Another interesting observation can be done if we plug the equation for the subscales (12) into the expression for num (17) (again taking into account the orthogonality of the subscales and neglectingp and µ∆u h ):…”

“…Its particularity is that it models the numerical subscales in a rich manner: the subscales are considered to be transient in time, non-linear, and orthogonal to the finite element space. A theoretical analysis of the orthogonal-subscales VMS turbulence model is presented in [24], and an extensive campaign of numerical experiments is presented in [19]. The conclusions of these experiments are that VMS turbulence models can provide an accurate representation of turbulent phenomena at a competitive computational cost, with the particular feature that the turbulence model arises from numerical reasoning only.…”

Efficient and scalable discretization of the Navier–Stokes equations with LPS modeling

“…Other similar studies can be found in the literature, but they always differ in some aspects with respect to the present work. In [29], a balancing Neumann-Neumann domain decomposition method is used for preconditioning the GMRES iterative method applied to the fully implicit monolithic system associated to a residual-based Orthogonal Subscales (OSS) modeling of the NSE. In [39], algebraic multigrid strategies for VMS-LES modeling are discussed, where a Smagorinsky-type eddy viscosity model is required.…”