Determining the Number of Grids for the Mann Uniform Shear Turbulence Model

In Mann model, the number of FFT points is important to ensure the quality of the spectra is satisfactory (see Verification of the Mann Uniform Shear Turbulence Model). Since the mann model calculations are done at the grid defined by the FFT points and the outputted at grid points defined by users (see Description of the Mann Uniform Shear Turbulence Model), the coherence at the neighbouring grid can be affected by the ratio of the FFT points to the grid points.

To demonstrate this effect and to provide a proper guideline about the number of grid points, Figure 1 can be used as the reference. It can be clearly seen that the coherence evaluated at the adjacent grid starts to deviate in comparison to the theoretical value once \(N^{FFT}/(N_{Max}-1)\) decreases. Here \(N_{Max}\) represents the maximum grid of the two spatial distances, lateral and vertical, or \(\max(N_y,N_z)\). To ensure the coherence is evaluated correctly at the adjacent grid, it is therefore recommended to ensure \(N^{FFT}/(N_{Max}-1) > 1.28\).

Figure 1: The effects of the number of FFT points and the resulting grid ratio on the coherence characteristics of the Mann model. Separation distance \(r\) is equal to the distance between adjacent grid points (\(N_{separation} = 1\)).

Last updated 17-07-2024