Optimal LES: How Good Can an LES Be?

In this paper, we approach Large Eddy Simulation (LES) by asking: How good is it possible for an LES to be? Taking a probabilistic approach, it is shown that by formally minimizing the rms error in the time derivative of the large scales, one can guarantee that the LES will reproduce the large scale statistics exactly. The LES model that minimizes the rms error in the time derivative is written as a conditional average, and we consider this to be the ideal LES model. Unfortunately, we do not know, nor can we practically compute this conditional average. The problem of LES modeling can therefore be considered to be a problem of finding a good approximation to the conditional average. Using direct numerical simulation data from a forced isotropic turbulence and a turbulent channel, estimates of the conditional average have been obtained, and the results are very instructive. Using the results, the nature of good LES models, the effects of filter definition, and the impact of inhomogeneity are explored. Also discussed is a program for developing practical LES models based on these ideas.

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