An introduction to Large Eddy Simulation (LES) of Turbulent Flows (Part I)

Turbulence is ubiquitous in nature and central to many applications important to our life. Obtaining an accurate prediction of turbulent flow is a central difficulty in such diverse problems as global change estimation, improving the energy efficiency of engines, controlling dispersal of contaminants and designing biomedical devices. It is absolutely fundamental to understanding physical processes of geophysics, combustion, forces of fluids upon elastic bodies, drag, lift and mixing. In these lectures we introduce one of the most promising numerical methods for the study of turbulent flows: Large Eddy Simulation (LES). LES seeks to calculate the large, energetic structures (the large eddies) in a turbulent flow. The aim of LES is to do this with complexity independent of the Reynolds number and dependent only on the resolution sought. The first lecture is devoted to an introduction to the problem of modeling and to the analysis of “eddy viscosity models” originated by the work of Smagorinsky and Ladyzhenskaya. In the second lecture we present advanced methods that are based on wavenumber asymptotics. Results of numerical experiments are also shown. In the third lecture we make an overview of recent advances as: filtering on bounded domains, near wall modeling, and variational multiscale methods.