Abstract
This chapter discusses direct numerical simulation (DNS) study of canonical turbulence. Incompressible turbulence obeying the Navier–Stokes (N–S) equation under periodic boundary conditions (BC) is widely regarded as one of the most canonical types of turbulences. It keeps the essence of tile turbulence dynamics: (1) the nonlinear convection effect associated with the fluid motion, (2) dissipativity, and (3) mass conservation, which is equivalent to the incompressibility or the so-called solenoidal condition in incompressible fluid. Underlying the study of turbulence in such a simple geometry is the idea of the Kolmogorov hypotheses, according to which the small scale statistics in fully developed turbulence at sufficiently high Reynolds number Re is universal and insensitive to the details of large scale conditions. The DNS of incompressible homogeneous turbulence was performed under periodic boundary conditions with the number of grid points up to 10243 on the VPP5000 system at the Information Technology Center, Nagoya University, and DNS up to 40963 grid points on the earth simulator (ES). The DNS is based on a spectral method free from alias error. Sustained performance of 16.4 Tflops was achieved in the DNS with 20483 grid points and double precision arithmetic on the ES.
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