Comparison of a spectral method with a higher-order finite difference method in direct numerical simulations of three-dimensional homogeneous turbulence

A finite difference method (FDM) is easier and cheaper to use than a spectral method (SM) in flows with complicated geometry, but is inferior to a SM in both accuracy and resolution. In this paper, effects of both accuracy and resolution in a FDM on the quality of incompressible turbulent flow description were studied by comparing a SM with a FDM in direct numerical simulations (DNS) of the three-dimensional freely decaying homogeneous turbulence with 128³ and 256³ grids. We adopted the higher-order method of lines and Fourier spectral method as a FDM and a SM, respectively. The value of the kinematic viscosity was determined so that the minimum value of K_maxη in time was about 2 in the SM with 256³ grids. Here, K_max and η are the maximum resolved wavenumber and the Kolmogorov length scale, respectively. The statistical quantities, such as the total energy, the energy dissipation ratio, obtained by the higher-order method of lines were in good agreement with those by the SM. Furthermore, comparing their DNS fields, we found that the performance of the 4th-order method of lines with 256³ grids was comparable to that of the SM with 128³ grids in which the minimum value of K_maxη in time was about 1.