CFD | DNS

DNS

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov microscales), up to the integral scale \(L\), associated with the motions containing most of the kinetic energy.

In fluid dynamics, Kolmogorov microscales are the smallest scales in turbulent flow. At the Kolmogorov scale, viscosity dominates and the turbulence kinetic energy is dissipated into thermal energy.

Term	Formula
Kolmogorov length scale	\(\eta = \left( \frac{\nu^3}{\varepsilon} \right)^{1/4}\)
Kolmogorov time scale	\(\tau_\eta = \sqrt{ \frac{\nu}{\varepsilon} }\)
Kolmogorov velocity scale	\(u_\eta = \left( \nu \varepsilon \right)^{1/4}\)

where

• \(\varepsilon\) is the average rate of dissipation of turbulence kinetic energy per unit mass, and
• \(\nu\) is the kinematic viscosity of the fluid.

References

1. 湍流是什么？（2）涡太小，量太大，值难算