Overview of DNS, LES, and RANS Turbulence Models

Direct Numerical Simulation (DNS) DNS requires no modeling, but it demands resolution from the large scales all the way through at least the beginning of the dissipation scales. As a result, this approach requires a significant amount of computational resources, leading to a total arithmetic scaling of at least Re^3.

Large Eddy Simulation (LES) LES requires modeling of part of the inertial subrange and into the beginning of the dissipation scales. The amount of required modeling is determined by the amount of resolution that can be afforded, but it is unlikely that the total arithmetic will scale worse than Re^2.

Reynolds-Averaged Navier-Stokes (RANS) RANS requires modeling everything from the integral scales into the dissipation range, with only mean (zero th –mode) quantities being directly computed. Consequently, the total arithmetic is, at most, a weak function of the Reynolds number (Re), meaning that the computational cost does not increase significantly with increasing Reynolds number.