# Direct Numerical Simulation

Direct Numerical Simulation (DNS) solves the time dependent Navier-Stokes equations, resolving from the largest length scale of a computational domain size to the smallest length scale of turbulence eddy (Kolmogorov length scale).

Considering a vast range of length scales within the computational domain, you can rightly claim that huge computer resource would be required for DNS. Examining the computer resource requirements for DNS will support this claim.

where $U$ is the characteristic velocity.

For a flat plate, turbulent flow occurs when the Re > 500,000 (Schlichting and Gersten, 2000). The above relation shows the estimation of six trillion nodes, which easily exceeds the capacity of even the most advanced high performance computers.

Therefore, the computational cost for DNS is very expensive, confirming that DNS is not feasible for high Reynolds Number turbulent flows.

In addition, high-order (third-order or higher) numerical schemes are commonly used in order to reduce the numerical dissipation and to keep the problem size tractable. These include spectral methods or spectral element methods. Although these methods are very efficient in resolving the small scales of turbulence, they require that the computational domain be relatively simple. The direct result is that these high-order schemes have little flexibility in dealing with complex industrial geometries because of the structured (blocked) mesh approach. Finally, DNS requires special treatments for realistic initial and boundary conditions

Considering these observations it can be concluded that DNS attempting to resolve all turbulent length and time scales is restricted to the low Reynolds number range and is impractical for industrial flows due to huge computing resource requirements. Most DNS applications are served as benchmark databases for tuning turbulence models and have been used for fundamental turbulent flow studies, including homogeneous turbulent flows with mean strain, free shear layers, fully developed channel flows, jets and so on.