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# Large eddy simulation

Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow.It was formulated in the late 1960s and became popular in the later years.It was first used by Joseph Smagorinsky to simulate atmospheric air currents, so its primary use at that time was for meteorological calculations and predictions. During the 80s and 90s it became widely used in the field of engineering.

A common deduction of Kolmogorov's (1941) famous theory of self similarity is that large eddies of the flow are dependent on the flow geometry, while smaller eddies are self similar and have a universal character. For this reason, it became a practice to solve only for the large eddies explicitly, and model the effect of the smaller and more universal eddies on the larger ones. Thus, in LES the large scale motions of the flow are calculated, while the effect of the smaller universal scales (the so called sub-grid scales) are modeled using a sub-grid scale (SGS) model. In practical implementations, one is required to solve the filtered Navier-Stokes equations with an additional sub-grid scale stress term. The most commonly used SGS models are the Smagorinsky model and its dynamic variants. They compensate for the unresolved turbulent scales through the addition of an "eddy viscosity" into the governing equations.

LES requires less computational effort than direct numerical simulation (DNS) but more effort than those methods that solve the Reynolds-averaged Navier-Stokes equations (RANS). The computational demands also increase significantly in the vicinity of walls, and simulating such flows usually exceeds the limits of modern supercomputers today.That's why we can call LES as "best of both worlds". For this reason, zonal approaches are often adopted, with RANS or other empirically-based models replacing LES in the wall region.

The main advantage of LES over computationally cheaper RANS approaches is the increased level of detail it can deliver. While RANS methods provide "averaged" results, LES is able to predict instantaneous flow characteristics and resolve turbulent flow structures. This is particularly important in simulations involving chemical reactions, such as the combustion of fuel in an engine. While the "averaged" concentration of chemical species may be too low to trigger a reaction, instantaneously there can be localised areas of high concentration in which reactions will occur. LES also offers significantly more accurate results over RANS for flows involving flow separation or acoustic prediction.

References

*Moeng, C-H, 1984: A Large-Eddy Simulation Model for the Study of Planetary Boundary-Layer turbulence. J. Atmos. Sci., 41, 2052-2062.

*Moeng, C-H., and Wyngaard, J.C. 1988: Spectral Analysis of Large-Eddy Simulations of the Convective Boundary layer. J. Atmos. Sci., 45, 3573-3587.

*Sullivan, P. P., J. C. McWilliams, and C.-H. Moeng, 1996: A grid nesting method for large-eddy simulation of planetary boundary layer flows. Boundary-Layer Meteorology, 80, 167-202.

*Moeng, C-H. and P.P. Sullivan, 2002: Large Eddy Simulation. In: Encyclopedia of Atmospheric Sciences, 1140-1150.

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