Accuracy and computational efficiency of dealiasing schemes for the DNS of under resolved flows with strong gradients

摘要

In this paper, we have studied the effect of residual aliasing error of the second order Runge-Kutta (RK2) based Random Phase Shift Method (RPSM) which shows smoothing effect in the solution of under-resolved flows involving strong gradients. Firstly, we show that RPSM is almost as accurate as the fully dealiased 3/2 Padding scheme but with similar computational cost as the fast 2/3 Truncation scheme. Secondly, we show that RPSM has high accuracy in the case of under-resolved shear layer and Surface Quasi-Geostrophic (SQG) flows. Further, we show that the 2/3 Truncation scheme turns more computationally expensive than 3/2 Padding or RPSM when we try to achieve the same level of accuracy. Filtering based dealiasing schemes are found to be an inappropriate choice for a variety of flow problems because they are prone to unphysical parasitic currents. For the first time error norm based computational efficiency, i.e., high accuracy at the lower computational cost of RPSM scheme is shown. Although some artifacts of dealiasing remain due to Fourier windowing in RPSM, it is found to be numerically stable even in under-resolved conditions at later simulation time. We have validated our numerical results with the analytical ones and also with the previous literature.