Subgrid-Scale modeling

Abstract
The purpose of this lecture is to give an overview of the subgrid scale models used for Large Eddy Simulations (LES). The first models where essentially eddy-viscosity models, where the turbulent viscosity coefficient was found by simple dimensional considerations (the mixing length theory) or taking into account Kolmogorov theory (the Smagorinsky model). Since then there have been many improvements, and now some of the physical ingredients of turbulence, such as the local backscatter and the anisotropy of small scale structures, can be successfully taken into account. Far from being a black box tool to obtain answers to turbulent flow problems, the Large Eddy Simulation technique is still a work in progress with many odds and ends. We give in this lecture an overview of the historical development of turbulence models and we point out the lights and shadows of them with attention to the open problems that still remain to be solved.