, is similar to the symmetry plane. In this case, however, the face values of the tensor in the coordinate system parallel to the axis are as follows:
On an axis boundary, the procedure for setting the specific Reynolds stress tensor at the face, , is similar to the symmetry plane. In this case, however, the face values of the tensor in the coordinate system parallel to the axis are as follows:
| (328) |
On a symmetry boundary, the procedure for setting the specific Reynolds stress tensor at the face, 
, is as follows. First, the tensor at the adjacent cell center, 
, is rotated such that it is parallel to the symmetry plane to obtain a new tensor termed 
. The symmetry boundary face values of the tensor in this rotated coordinate system are explicitly set as follows:
| (329) |
The values of 
are computed by rotating the 
tensor back to the original orientation of 
. (This is made easy by the fact that the inverse of the rotation tensor is simply its transpose, since it is an orthogonal tensor.)
At walls, a Neumann boundary condition is used for the Reynolds stresses 
, that is, 
. In addition, a method developed by Hadzic [45] is used to impose the value of production of each stress component in accordance with a wall function approach. This method is summarized here.
In a coordinate system oriented with the wall, the production of turbulent kinetic energy is
| (330) |
where 
is the wall-normal velocity gradient. If one obtains the production 
and the shear stress 
from wall functions, and assumes that all gradients other than 
are negligible, a velocity gradient tensor in the wall-oriented coordinates may be constructed as follows:
| (331) |
The velocity gradient tensor in Cartesian coordinates is then obtained by rotating 
using the appropriate tensor transformation.
If this technique is used with a consistent method of evaluating 
so as to satisfy local equilibrium (
), this method will ensure the correct ratios of Reynolds stress to turbulent kinetic energy in a local equilibrium situation. However, it will allow the stress values to vary whenever a non-equilibrium situation is encountered.
When defining values for flow boundary, region and initial conditions, you have several choices for specifying the Reynolds stress tensor and the isotropic dissipation rate:
where 
is the supplied turbulent kinetic energy and 
is the identity matrix.
| (332) |
and turbulent length scale 
using the relations:
using the relations: