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## Direct numerical simulationA ## Additional recommended knowledge
where ν is the kinematic viscosity and ε is the rate of kinetic energy dissipation. On the other hand, the integral scale depends usually on the spatial scale of the boundary conditions. To satisfy these resolution requirements, the number , so that the integral scale is contained within the computational domain, and also , so that the Kolmogorov scale can be resolved. Since , where
where Re is the turbulent Reynolds number . Hence, the memory storage requirement in a DNS grows very fast with the Reynolds number. In addition, given the very large memory necessary, the integration of the solution in time must be done by an explicit method. This means that in order to be accurate, the integration must be done with a time step, Δt, small enough such that a fluid particle moves only a fraction of the mesh spacing
( The total time interval simulated is generally proportional to the turbulence time scale τ given by . Combining these relations, and the fact that , and consequently, the number of time steps grows also as a power law of the Reynolds number. One can estimate that the number of floating-point operations required to complete the simulation is proportional to the number of mesh points and the number of time steps, and in conclusion, the number of operations grows as Re 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 computers 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. Also, 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. The biggest DNS in the world, up to this date, used 4096 ## See also |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Direct_numerical_simulation". A list of authors is available in Wikipedia. |