ABSTRACT
John A. Ekaterinaris, School of Mechanical and Aerospace Engineering, University of Patras, Greece and Foundation for Research and Technology-Hellas, Institute of Applied and Computational Mathematics, 71110 Heraklion, Greece, ekaterin@iacm.forth.gr
In the past, efforts were made towards developing high-order finitedifference (FD) methods in the areas direct and large eddy simulations. For nonlinear problems, straightforward application of high-order accurate central difference schemes is not possible, because the spurious modes that develop from the unresolvable by the numerical discretization high frequency modes lead to instabilities. Rai and Moin [146] found that high-order upwind schemes are more promising to simulate turbulent flows. However, early attempts to apply high-order finite differences were often frustrated because of lack of robustness of the proposed high-order (FD) schemes compared to spectral methods. For example, it was found [146] and references therein) that:
1. For DNS with energy conserving FD schemes the actual energy transfer toward large wave numbers in the simulation is too large;
2. Spectral methods have the advantage to signal their accuracy or inaccuracy through an inadequately resolved enstrophy dissipation spectrum whereas FD schemes do not and;
3. Spectral methods require roughly half as much resolution as FD schemes in each spatial direction to yield solutions of comparable accuracy.
