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In Large-Eddy Simulations, the instantaneous velocity U(x,t) is decomposed into a filtered component Ū(x,t) and a residual component u'(x,t). The filtered velocity component represents the large scale unsteady motions. The In LES, the large scale turbulent motions are directly represented whereas the effects of small scale turbulent motions are modeled. The filtered equations for the filtered velocity can be obtained from the Navier-Stokes equations. Hence, in LES the large scale turbulent motions are exactly solved while the small scale turbulent motions are modeled. The non-linear convective term in the momentum equation introduces a residual stress tensor which is due to the residual motions. Closure is needed for this residual stress tensor and hence require modeling. There are simple to complex models in FLUENT which will use soon.

Since we are solving for Ū(x,t), the LES is an unsteady simulation where we march in time. In order to collect statistics like the mean and root mean square (r.m.s.) velocities, we need to first reach a statistically stationary state. In comparison, simulation using k-ε model solves only for the mean velocity.

More information on the LES can be found in Turbulent Flows by Pope\[2000\].

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