Spalart–Allmaras turbulence model
In physics, the Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity. The Spalart–Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity in turbomachinery applications. In its original form, the model is effectively a low-Reynolds number model, requiring the viscosity-affected region of the boundary layer to be properly resolved ( y+ ~1 meshes). The Spalart–Allmaras model was developed  for aerodynamic flows. It is not calibrated for general industrial flows, and does produce relatively larger errors for some free shear flows, especially plane and round jet flows. In addition, it cannot be relied on to predict the decay of homogeneous, isotropic turbulence. It solves a transport equation for a viscosity-like variable formula_1. This may be referred to as the "Spalart–Allmaras variable". Original model. The turbulent eddy viscosity is given by The rotation tensor is given by where d is the distance from the closest surface and formula_10 is the norm of the difference between the velocity  at the trip (usually zero) and that at the field point we are considering. The constants are Modifications to original model. 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) DDES (2006) Model for compressible flows. There are two approaches to adapting the model for compressible flows. In the first approach, the turbulent dynamic viscosity is computed from where formula_14 is the local density. The convective terms in the equation for formula_1 are modified to where the right hand side (RHS) is the  same as in the original model. Boundary conditions. Walls: formula_17 Freestream: Ideally formula_17, but some solvers can have problems with a zero value, in which case formula_19 can be used. This is if the trip term is used to "start up" the model. A convenient option is to set formula_20 in the freestream. The model then provides "Fully Turbulent" behavior, i.e., it becomes turbulent in any region that contains shear. Outlet: convective outlet.