Abstract

In this paper we analyze a stabilized finite element approximation for the incompressible Navier–Stokes equations based on the subgrid-scale concept. The essential point is that we explore the properties of the discrete formulation that results allowing the subgrid-scales to depend on time. This apparently “natural” idea avoids several inconsistencies of previous formulations and also opens the door to generalizations.

Abstract

In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented.