4.3.2 Transport Equation for the Spalart-Allmaras Model

The transported variable in the Spalart-Allmaras model, $\widetilde{\nu}$, is identical to the turbulent kinematic viscosity except in the near-wall (viscosity-affected) region. The transport equation for $\widetilde{\nu}$ is

where $G_\nu$ is the production of turbulent viscosity, and $Y_\nu$ is the destruction of turbulent viscosity that occurs in the near-wall region due to wall blocking and viscous damping. $\sigma_{\widetilde{\nu}}$ and $C_{b2}$ are the constants and $\nu$ is the molecular kinematic viscosity. $S_{\widetilde{\nu}}$ is a user-defined source term. Note that since the turbulence kinetic energy, $k$, is not calculated in the Spalart-Allmaras model, while the last term in Equation  4.2-5 is ignored when estimating the Reynolds stresses.