Spalart-Allmaras

Properties

  • One equation model based on a modified turbulence viscosity, \( \tilde{\nu} \)

Model equations

\[ \Ddt{\rho \tilde{\nu}} = \div \left( \rho D_\tilde{\nu} \tilde{\nu} \right) + \frac{C_{b2}}{\sigma_{\nu_t}} \rho \mag{\grad \tilde{\nu}}^2 + C_{b1} \rho \tilde{S} \tilde{\nu} \left(1 - f_{t2}\right) - \left(C_{w1} f_w - \frac{C_{b1}}{\kappa^2} f_{t2}\right) \rho \frac{\tilde{\nu}^2}{\tilde{d}^2} + S_\tilde{\nu} \]

Note
The \( f_{t2} \) term is not implemented.

The turbulence viscosity is obtained using:

\[ \nu_t = \tilde{\nu} f_{v1} \]

where the function \( f_{v1} \) is given by

\[ f_{v1} = \frac{\chi^3}{\chi^3 + C_{v1}^3} \]

and

\[ \chi = \frac{\tilde{\nu}}{\nu} \]

Default model coefficients

\( \sigma_{\nu_t} \) \( C_{b1} \) \( C_{b2} \) \( C_{w1} \) \( C_{w2} \) \( C_{w3} \)
2/3 0.1355 0.622 \(\frac{C_{b1}}{\kappa^2} + \frac{1 + C_{b2}}{\sigma_{\nu_t}} \) 0.3 2
\( C_{v1} \) \( C_{s} \)
7.1 0.3

Usage

The model is specified using:

RAS
{
    turbulence      on;
    RASModel        SpalartAllmaras;
}

Further information

Source code:

References:

  • Standard model: Spalart [72]

Related:


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