A disadvantage of standard two-equation turbulence models is the excessive generation of the
turbulence energy, 
, in the vicinity of stagnation points. In order to avoid the buildup of
turbulent kinetic energy in the stagnation regions, the production term in the turbulence
equations can be limited by one of the two formulations presented below.
The first formulation takes the following form (Menter [428]):
 | (4–436) |
where the coefficient 
has a default value of 10. This limiter does not affect the shear layer
performance of the model, but avoids the stagnation point buildup in aerodynamic simulations. The
first formulation is available for the following turbulence models:
Standard, RNG, and Realizable (
-
)-modelsStandard (
-
), BSL, SST, and Transition SSTScale-Adaptive Simulation (SAS)
Detached Eddy Simulation with BSL / SST (DES-BSL / SST) and with Realizable (
-
)-models (DES-rke)Shielded Detached Eddy Simulation (SDES)
Stress-Blended Eddy Simulation (SBES)
By default, this limiter is enabled for all turbulence models based on the 
equation.
Using the standard Boussinesq approximation for the Reynolds stress tensor, the production
term 
for an incompressible flow can be expressed as:
 | (4–437) |
where 
is the magnitude of the strain rate:
 | (4–438) |
The strain rate tensor 
is calculated as:
 | (4–439) |
The second formulation is based on the work of Kato and Launder ([293]) who noticed that the excessive level of turbulence
kinetic energy production is caused by the very high level of shear strain rate 
in the stagnation regions. As the flow field near a stagnation point is nearly
irrotational, with a very small vorticity rate 
, the alternative form of the production term proposed by Kato-Launder is written
as:
 | (4–440) |
where 
is the magnitude of the vorticity rate:
 | (4–441) |
where the vorticity tensor 
is calculated as:
 | (4–442) |
In a simple shear flow, 
and 
are equal and thus Equation 4–437 is
recovered. The Kato-Launder formulation for the production term is available for the following
turbulence models:
Standard, and RNG (
-
)-modelsStandard (
-
), BSL, SST, and Transition SSTScale-Adaptive Simulation (SAS)
Detached Eddy Simulation with BSL / SST (DES-BSL / SST)
Shielded Detached Eddy Simulation (SDES)
Stress-Blended Eddy Simulation (SBES)
The Kato-Launder formulation is enabled by default only for the Transition SST model.
Both modifications for the production term can be accessed in the Viscous Model panel. For more details, see Including Production Limiters for Two-Equation Models in the Fluent User's Guide. The Kato-Launder formulation and production limiter can be applied simultaneously, as is done for the Transition SST model by default.