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All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov scales), given by 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 and . Since , where ''u''' is the root mean square (RMS) of the velocity, the previous relations imply that a three-dimensional DNS requires a number of mesh points 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 methods that solve the Reynolds-averaged Navier-Stokes Equations (RANS). 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. SEE ALSO EXTERNAL LINK
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