Turbulent flows are characterized by eddies with a wide range of length and time scales. The largest eddies are typically comparable in size to the characteristic length of the mean flow (for example, shear layer thickness). The smallest scales are responsible for the dissipation of turbulence kinetic energy.
It is possible, in theory, to directly resolve the whole spectrum of turbulent scales using
an approach known as direct numerical simulation (DNS). No modeling is required in DNS. However,
DNS is not feasible for practical engineering problems involving high Reynolds number flows. The
cost required for DNS to resolve the entire range of scales is proportional to 
, where 
is the turbulent Reynolds number. Clearly, for high Reynolds numbers, the cost
becomes prohibitive.
In LES, large eddies are resolved directly, while small eddies are modeled. Large eddy simulation (LES) therefore falls between DNS and RANS in terms of the fraction of the resolved scales. The rationale behind LES can be summarized as follows:
Momentum, mass, energy, and other passive scalars are transported mostly by large eddies.
Large eddies are more problem-dependent. They are dictated by the geometries and boundary conditions of the flow involved.
Small eddies are less dependent on the geometry, tend to be more isotropic, and are consequently more universal.
The chance of finding a universal turbulence model is much higher for small eddies.
Resolving only the large eddies allows one to use much coarser mesh and larger time-step
sizes in LES than in DNS. However, LES still requires substantially finer meshes than those
typically used for RANS calculations. In addition, LES has to be run for a sufficiently long
flow-time to obtain stable statistics of the flow being modeled. As a result, the computational
cost involved with LES is normally orders of magnitudes higher than that for steady RANS
calculations in terms of memory (RAM) and CPU time. Therefore, high-performance computing (for
example, parallel computing) is a necessity for LES, especially for industrial applications. The
main shortcoming of LES lies in the high resolution requirements for wall boundary layers. Near
the wall, even the ‘large’ eddies become relatively small and require a Reynolds
number dependent resolution. This limits LES for wall bounded flows to very low Reynolds numbers
(
) and limited computational domains.
The following sections give details of the governing equations for LES, the subgrid-scale turbulence models, and the boundary conditions.