I am learning about fourier analysis of turbulence, which eventually i will be analysing in an LES approach.

I have read in many book now the idea of convolution, and of its importance especially in LES.

I do not understand convolution!!! nor do i readly understand its importance.

Can anyone give me a brief statement of the importance of convolution, and refer me to a book i could look at.

Thanks

Large Eddy Simulation = Simulation only large eddies and model small eddies.

How to define large and small eddies --> filtering.

Filtering is a kind of convolution.

In LES, velocity fields are filtered and only grid scales (or filtered scales) are calculated and subgrid scales are modeled (such as dynamic model, etc) using grid scale information.

If the velocity fields are stationary, you can use fourier convolution scheme. Actually convolution is integration and not easy to calculate. But if the velocity fields are transformed to wave number(or frequency) space, the convolution could be transformed to simple algebraic equations. Using FFT, the calculation is very fast.

Reference material of the convolution : Chapter 12 Large eddy simulations, 12.2 Filtering of " Fluid Flow Phenomena", A numerical Toolkit, by P. Orlandi.