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Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and many of the issues unique to LES were first explored by Deardorff (1970). LES grew rapidly beginning with its invention in the 1960s and is currently applied in a wide variety of engineering applications, including combustion, acoustics, and simulations of the atmospheric boundary layer. LES operates on the Navier–Stokes equations to reduce the range of length scales of the solution, reducing the computational cost.

The principal operation in large eddy simulation is low-pass filtering. This operation is applied to the Navier–Stokes equations to eliminate small scales of the solution. This reduces the computational cost of the simulation. The governing equations are thus transformed, and the solution is a filtered velocity field. Which of the “small” length and time scales to eliminate are selected according to turbulence theory and available computational resources.

Large eddy simulation resolves large scales of the flow field solution allowing better fidelity than alternative approaches such as Reynolds-averaged Navier–Stokes (RANS) methods. It also models the smallest (and most expensive) scales of the solution, rather than resolving them as direct numerical simulation (DNS) does. This makes the computational cost for practical engineering systems with complex geometry or flow configurations, such as turbulent jets, pumps, vehicles, and landing gear, attainable using supercomputers. In contrast, direct numerical simulation, which resolves every scale of the solution, is prohibitively expensive for nearly all systems with complex geometry or flow configurations.