Direct Numerical Simulation

The direct numerical simulation is the most elegant way to simulate turbulence since no major assumptions and no closure equations are needed (Moin and Mahesh (1998)). The classical Navier-Stokes, continuity, and energy equations are solved directly using a high-order convective scheme. In practice, a grid scale on the order of five times the Kolmogorov scale is usually utilized (except in the near-wall region). It is a common practice to use higher order schemes for the convective terms in DNS. Typically, the fifth order scheme of Rai and Moin (1991) uses a seven point stencil. The scheme is expressed as

	(36.1)

The DNS studies are limited by the computational means. Let us consider the landmarks of DNS research:

1. Kim et al. (1987) studied a turbulent channel flow with a 192×129×160 grid-mesh (Re = 3300)
   
2. Spalart (1989) studied a turbulent boundary layer at Re = 1410 with a 432 × 80 × 320 grids.
   
3. Le et al. (1997) conducted a direct numerical simulation for backward facing step flow for a Reynolds number of 5100 using 768 × 192 × 64 grids.

The main applications of DNS are (i) to provide reliable data for the validation of turbulence models; (ii) to provide data for evaluation of subgrid models for LES; and (iii) to discover fundamental physics of turbulence. Even supercomputers have limited capability for performing DNS of complex flows in the turbomachinery or heat exchangers.