Complexity scaling of finite surface method in high Reynolds number flows

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A. Hokpunna


This paper investigates the complexity scaling of the finite surface (FS) discretization applied to Navier-Stokes equations. The previous work on the turbulent channel flow suggests that the grids resolutions needed to achieve 1%-error in the first- and the second-order statistics is 30 and 11 wall-unit in the streamwise- and spanwise-directions. This grid size is about 10-times larger than the traditional recommendation and requires much lower computational resources. In this work, we investigate the application of this new resolution to the Reynolds number cases: Ret = 180, 390, 590, and 950. The mean and the RMS of the fluctuations are presented and compared with results from spectral codes. The result of the investigation indicates that the finite surface method can deliver a 1%-accurate prediction in the mean profile of turbulent channel flows using this resolution. Effectively, the number of grid points for 1%-accurate prediction scales with (Ret/22)3+(Ret/5.4)2.


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