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Abstract-
Large eddy simulation (LES) is a promising technique for the
prediction of turbulent fluid flows of practical interest. In LES, the
largest scales of turbulence are simulated while the effects of the
discarded small scales are modeled. However, there are important flow
situations, such as turbulence near walls, that current LES techniques
do not simulate reliably. To address these difficulties, the
fundamental formulation of LES has be reexamined, and a new modeling
approach has been developed. In our new formulation, stochastic
estimation techniques can be used to formally optimize the LES
model. This yields an approximation to the ideal LES evolution, which
is guaranteed to reproduce the single-time statistics of the filtered
turbulence, and to minimize the expected difference between the
evolution of a filtered turbulence and the LES. Using direct numerical
simulation (DNS) statistical data to perform the estimates, several
such models have been formulated for different turbulent flows and
different LES filter definitions. These models perform remarkably
well. They also yield important insights into the required properties
of good LES models. To make these models useful however, it is
necessary to eliminate the need for detailed statistical data from
DNS. When the small scales are assumed to be isotropic, this can be
accomplished through a combination of Kolmogorov inertial range
scaling, the quasi-normal approximation and a dynamic procedure, and
the resulting model is as accurate as that based on DNS data. Near
walls, a variety of other theoretical considerations significantly
constrain the required statistics, and using this, a formulation
requiring minimal empirical input is being devised.
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