On Implicit Subgrid Scale Modeling for Turbulent Flows

Large Eddy Simulation (LES) is an effective intermediate approach between DNS and RANS, capable of simulating flow features which cannot be handled with RANS such as significant flow unsteadiness and strong vortex-acoustic couplings, and providing higher accuracy than RANS at reasonable cost but still typically an order of magnitude more expensive. Desirable modeling choices involve selecting an appropriate discretization of the flow problem at hand, such that the LES cut-off lies within the inertial sub-range, and ensuring that a smooth transition can be enforced at the cut-off. The main assumptions of LES are: (i) that transport is largely governed by large-scale unsteady features and that such dominant features of the flow can be resolved, (ii) that the less-demanding accounting of the small-scale flow features can be undertaken by using suitable Sub Grid Scale (SGS) models. In the absence of an accepted universal theory of turbulence, the development and improvement of SGS models are unavoidably pragmatic and based on the rational use of empirical information. Classical approaches have included many proposals ranging from, inherently-limited eddy-viscosity formulations, to more sophisticated and accurate mixed models, e.g., [1]. For the sake of the discussion, we restrict ourselves to the incompressible regime, and focus on the crucial LES closure issue of modeling the SGS stress tensor,