Finite Difference vs. Spectral Methods

In a comparative study, Rai & Moin [14] examined the influence of a finite difference vs. a spectral approach on the statistical results by comparing the turbulence statistics of their earlier computations using spectral methods (Kim et al. [6]) with those obtained using various finite difference techniques. They concluded that the prevalent method for DNS of turbulent flows is the spectral method, but that for complex geometries, finite difference techniques, especially high-order accurate upwind-biased methods, are good candidates. The statistical results obtained from the finite difference computations showed a reasonable but not excellent agreement with the results obtained earlier with the spectral method. However this is not sufficient to justify a conclusion on the performance of finite difference schemes, as the total number of grid points used for the finite difference computations was just $35 \%$ of those used for the spectral method.