The governing equations employed for LES are obtained by filtering the
time-dependent Navier-Stokes equations in either Fourier (wave-number) 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
is the fluid domain, and
is the filter function
that determines the scale of the resolved eddies.
FLUENT, the finite-volume discretization itself implicitly
provides the filtering operation:
is the volume of a computational cell.
The filter function,
, implied here is then
The LES capability in
FLUENT is applicable to compressible flows.
For the sake of concise notation, however, the theory is presented here for incompressible flows.
Filtering the Navier-Stokes equations, one obtains
is the stress tensor due to molecular viscosity defined by