The Spalart–Allmaras model is a one equation model for the turbulent viscosity. It solves a transport equation for a viscosity-like variable . This may be referred to as the Spalart–Allmaras variable.
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The turbulent eddy viscosity is given by
The rotation tensor is given by
and d is the distance from the closest surface.
The constants are
According to Spalart it is safer to use the following values for the last two constants:
Other models related to the S-A model:
DES (1999) [1]
DDES (2006)
There are two approaches to adapting the model for compressible flows. In the first approach the turbulent dynamic viscosity is computed from
where is the local density. The convective terms in the equation for are modified to
where the right hand side (RHS) is the same as in the original model.
Walls:
Freestream:
Ideally , but some solvers can have problems with a zero value, in which case can be used.
This is if the trip term is used to "start up" the model. A convenient option is to set in the freestream. The model then provides "Fully Turbulent" behavior, i.e., it becomes turbulent in any region that contains shear.
Outlet: convective outlet.