
Timedependent solutions of the NavierStokes equations for
high Reynoldsnumber turbulent flows in complex geometries which
set out to resolve all the way down to the smallest scales of the motions are
unlikely to be attainable for some time to come. Two alternative methods can be
employed to render the NavierStokes equations tractable so that the smallscale
turbulent fluctuations do not have to be directly simulated: Reynoldsaveraging
(or ensembleaveraging) and filtering. Both methods introduce additional terms in the governing
equations that need to be modeled in order to achieve a "closure'' for the unknowns.
The Reynoldsaveraged NavierStokes (RANS) equations govern the transport of the averaged
flow quantities, with the whole range of the scales of turbulence being modeled.
The RANSbased modeling approach therefore greatly reduces the required computational effort and resources,
and is widely adopted for practical engineering applications. An entire hierarchy of closure models
are available in
FLUENT including SpalartAllmaras,

and its variants,

and its variants,
and the RSM. The RANS equations are often used to compute timedependent flows, whose unsteadiness may
be externally imposed (e.g., timedependent boundary conditions or sources) or selfsustained
(e.g., vortexshedding, flow instabilities).
LES provides an alternative approach in which large eddies are explicitly computed (resolved) in a
timedependent simulation using the "filtered'' NavierStokes equations. The rationale behind LES is that
by modeling less of turbulence (and resolving more), the error introduced by turbulence modeling can be reduced.
It is also believed to be easier to find a "universal'' model for the small scales, since they tend to be more
isotropic and less affected by the macroscopic features like boundary conditions, than the large eddies.
Filtering is essentially a mathematical manipulation of the exact NavierStokes equations to remove the
eddies that are smaller than the size of the filter, which is usually taken as the mesh size when spatial
filtering is employed as in
FLUENT. Like Reynoldsaveraging, the filtering process creates
additional unknown terms that must be modeled to achieve closure. Statistics of the timevarying flowfields
such as timeaverages and r.m.s. values of the solution variables, which are generally of most engineering interest,
can be collected during the timedependent simulation.
LES for high Reynolds number industrial flows requires a significant amount of compute resources.
This is mainly because of the need to accurately resolve the energycontaining turbulent eddies
in both space and time domains, which becomes most acute in nearwall regions where the scales to be
resolved become increasingly smaller. Wall functions in combination with a coarse near wall mesh can be employed,
often with some success, to reduce the cost of LES for wallbounded flows. However, one needs to carefully
consider the ramification of using wall functions for the flow in question. For the same reason (to accurately
resolve the eddies), LES also requires highly accurate spatial and temporal discretizations.