The Spalart-Allmaras model has been extended within Ansys Fluent with a 
-insensitive wall treatment, which automatically blends all solution variables
from their viscous sublayer formulation
 | (4–30) |
to the corresponding logarithmic layer values depending on 
.
 | (4–31) |
where 
is the velocity parallel to the wall, 
is the friction velocity, 
is the distance from the wall, 
is the von Kármán constant (0.4187), and 
.
The blending is calibrated to also cover intermediate 
values in the buffer layer 
.
On the basis of the standard Spalart-Allmaras model equation, the Boeing Extension [33] has been adopted to account for wall roughness. In this model, the
non-zero wall value of the transported variable (directly solved from the S-A equation), 
, is estimated to mimic roughness effects by replacing the wall condition 
with:
 | (4–32) |
where 
is the wall normal, 
is the minimum cell-to-face distance between the wall and the first cell near
the wall, and 
is a length introduced to impose an offset, depending on the local roughness
height, 
:
 | (4–33) |
Then the wall turbulent kinematic viscosity, 
, is obtained as follows:
 | (4–34) |
where 
is the standard model function in the Spalart-Allmaras model. As the roughness
effect is strong, the turbulent viscosity should be large compared to the laminar viscosity at
the wall, then 
→ 1, and therefore:
 | (4–35) |
Also in Equation 4–34, 
is the Von Karman constant, and 
is the wall friction velocity:
 | (4–36) |
Furthermore, to achieve good predictions for smaller roughness, Aupoix and Spalart [33] proposed that the function 
should be altered by modifying the quantity 
in the Spalart-Allmaras model equation:
 | (4–37) |