Direct Numerical Simulation of Three-Dimensional Homogeneous Isotropic Turbulence by Higher-Order Finite Diffeerence Scheme. Comparison with the Spectral Method and the Experiment.

Abstract

A direct numerical simulation of three-dimensional homogeneous isotropic turbulence by the spectral method and the higher-order finite difference scheme (FDS) has been conducted with 64×64×64 and 96×96×96 grids. The energy spectrum obtained by the FDS is compared with that obtained by the spectral method and that obtained by the experiment to investigate the effect of discretization. From these studies, the following conclusions are obtained. (1) As for the discretization of the nonlinear term with the 64×64×64 grids, the energy spectrum obtained by the 5th-order upwind FDS coincides with those obtained by the spectral method and the experiment up to the cutoff wave number, while the 3rd-order upwind FDS shows deviation from those obtained by the spectral method and the experiment. (2) With the 64×64×64 grids, the 6th-order central FDS with the skew-symmetric form is valid for DNS, while the 6th-order central FDS with the convective form overestimates the energy in the region around the cutoff wave number. (3) With the nonlinear term discretized by the 5th-order upwind FDS or 6th-order central FDS with the skew-symmetric from, the 4th-order FDS is suitable for the viscous term.