Explanation: Large Eddy Simulation (LES) method is useful to capture the large turbulent eddies. It is not as accurate as the DNS method and not computationally demanding. As high Reynolds number will have large eddies, it is preferred when the flow has a high Reynolds number.

Explanation: Les captures large eddies only. So, spatial filtering is used to separate the large and small eddies. A filtering function and the cut-off width above which the flow will be solved are selected before solving the flow.

Explanation: During spatial filtering, the information about the small eddies will be lost. The interaction between large eddies and small eddies leads to this SGS stress. It stands for sub-grid-scale stress.

Explanation: The LES method uses a filter function to spatially filter and get the larger eddies of interest. The most common three-dimensional filters are Top-hat filter, Gaussian filter and Spectral cut-off filters.

Δ → Cut-off width

\(G(\vec{x},\vec{x’},\Delta)=(\frac{\gamma}{\pi \Delta^2})^{\frac{3}{2}} exp(-\gamma \frac{\big|\vec x,\vec{x’}\big|^2}{\Delta^2})\)

Explanation: The spectral cut-off filter is the product of \(\frac{sin[(x_i-x_i^{‘})]}{(x_i-x_i^{‘})}\) for all three directions of the x-vector. This gives a sharp cut-off in the energy spectrum at a wavelength of Δ/π.

Explanation: The top-hat or box filter is the one which is preferred for the finite volume methods in CFD packages. This is because of their simple elimination of small eddies. The Gaussian and spectral cut-off filter are used for research purposes.