
The governing equations employed for LES are obtained by filtering the timedependent NavierStokes equations in either Fourier (wavenumber) space or configuration (physical) space. The filtering process effectively filters out the eddies whose scales are smaller than the filter width or grid spacing used in the computations. The resulting equations thus govern the dynamics of large eddies.
A filtered variable (denoted by an overbar) is defined by
where
is the fluid domain, and
is the filter function that determines the scale of the resolved eddies.
In ANSYS FLUENT, the finitevolume discretization itself implicitly provides the filtering operation:
where is the volume of a computational cell. The filter function, , implied here is then
(4.113) 
The LES capability in
ANSYS FLUENT is applicable to compressible flows. For the sake of concise notation, however, the theory is presented here for incompressible flows.
Filtering the NavierStokes equations, one obtains
and
where
is the stress tensor due to molecular viscosity defined by
(4.116) 