Direct numerical simulation

Direct numerical simulation (DNS) solves the governing fluid equations while resolving all dynamically relevant motion scales, without using a turbulence model.

Navier–Stokes equations: The equations expressing conservation of momentum and mass in fluid motion. DNS computes fluid evolution by numerically solving these governing equations.
Homogeneous isotropic turbulence: An idealized turbulent flow whose statistics are uniform in space and direction. Its simple setting makes it a standard DNS case for studying turbulent statistics.
Large eddy simulation: A turbulence simulation method that resolves large flow structures and models smaller ones. Unlike DNS, it filters out and models motions below the chosen grid scale.
Kolmogorov 1941 theory: A theory describing universal statistical behavior of small scales in high-Reynolds-number turbulence. Its scale predictions helped define the fine motions DNS must capture.
Kolmogorov microscales: The smallest characteristic length and time scales of turbulence, where viscosity dissipates kinetic energy. DNS grids must resolve these scales to capture the end of the turbulent energy cascade.
Taylor–Green vortex: An analytical vortex-flow initial condition that evolves into complex three-dimensional turbulence. DNS of this benchmark tracks the transition from organized vortices to turbulent motion.
Reynolds-averaged Navier–Stokes equations: Equations for mean fluid motion that represent turbulent fluctuations through additional modeled stresses. RANS models the aggregate effects of turbulence rather than resolving its full range of scales.
John von Neumann: A mathematician and physicist who helped establish modern numerical weather prediction and computing. His work on numerical computation helped create the tools later used for fluid simulation.
Courant–Friedrichs–Lewy condition: A numerical stability condition linking time-step size to grid spacing and wave or flow speed. It constrains DNS time steps as well as the spatial resolution.
Turbulent channel flow: Turbulent flow driven through a channel between parallel walls. DNS resolves its near-wall structures and supplies data for wall-turbulence research.

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TurbulenceCompared with: It represents turbulence directly but becomes prohibitively expensive at high Reynolds numbers.