A direct numerical simulation (DNS) is a simulation in computational fluid dynamics 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 scales), given by A simulation is an imitation of some real device or state of affairs. ... Computational fluid dynamics (CFD) is the use of computers to analyze problems in fluid dynamics. ...

where ν is the kinematic viscosity and ε the kinetic energy dissipation, up to the integral scale L. To satisfy these conditions, the number N of points along a given mesh direction with increments h must satisfy

Nh > L

and

.

Since

,

where u' is the root mean square (RMS) of the velocity, the previous relations implies that a three-dimensional DNS requires a number of mesh points N³ satisfying

where Re is the turbulent Reynolds number

.

Therefore, the computational cost of DNS is very high, even at low Reynolds numbers. For the Reynolds numbers encountered in most industrial applications, the computational resources required by a DNS would exceed the capacity of the most powerful computer currently available. However, direct numerical simulation is a useful tool in fundamental research in turbulence. Using DNS it is possible to perform "numerical experiments", and extract from them information difficult or impossible to obtain in the laboratory, allowing a better understanding of the physics of turbulence. In addition, direct numerical simulations are useful in the development of turbulence models for practical applications, such as sub-grid scale models for Large eddy simulation (LES) and models for RANS solutions. This is done by means of "a priori" tests, in which the input data for the model is taken from a DNS simulation, or by "a posteriori" tests, in which the results produced by the model are compared with those obtained by DNS. Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow. ...

See also

• Large eddy simulation

Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow. ...

External link

• DNS page at CFD-Wiki