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12.3.2 Transport Equation for the Spalart-Allmaras Model

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

 \frac{\partial}{\partial t} (\rho \tilde{\nu}) + \frac{\par... ...}}{\partial x_j}\right)^2\right] - Y_\nu + S_{\tilde{\nu}} (12.3-1)

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. $\sigma_{\tilde{\nu}}$ and $C_{b2}$ are constants and $\nu$ is the molecular kinematic viscosity. $S_{\tilde{\nu}}$ is a user-defined source term. Note that since the turbulence kinetic energy $k$ is not calculated in the Spalart-Allmaras model, the last term in Equation  12.2-5 is ignored when estimating the Reynolds stresses.

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