Large Eddy Simulation (LES)

The most elegant approach to the solution of turbulent flows is the direct numerical simulation (DNS) of turbulence, in which the governing equations are discretized and solved numerically using extremely fine grid mesh. If the grid size is fine enough to resolve the smallest scale of motion, and the solution scheme is designed to minimize the numerical diffusion and dissipation errors, one can achieve an accurate three-dimensional, time-dependent solution of the governing equations completely free of modeling assumptions. Thus DNS has been a very useful tool, over the past ten years, for the study of transitional and turbulent flow physics, but it has a severe limitation. In order to resolve all scales of motion, one requires a number of grid points N ~ L / η , where L is the dimension of computational domain (basically the largest scale in the system) and η is the smallest scale in motion, the Kolmogorov length scale. Since this ratio is proportional to Re^3/4 , the number of grid point needed by a DNS is order of N³ ~ Re^9/4 . On the other hand the solutions of Reynolds-averaged equations using k - ε and any other suitable model have basic limitations because of the non-linear, non-local and non-Gaussian properties of turbulence. Large-Eddy Simulation (LES) is a technique, which draws the advantages of the direct simulation of turbulent flows and the solution of the Reynolds-averaged equations through closure assumptions. In LES, the contribution of the large-scale structures to momentum and energy transfer is computed exactly and the effect of the smallest scales of turbulence is modeled. Pioneering work on LES has been done by Deardorff (1970, 1971). Subsequently, different groups have achieved considerable progress. Schumann (1975), Moin and Kim (1982), Mason and Callen (1986), Schmidt and Schumann (1989), Piomelli (1993) are to name a few other early contributions.