The open source CFD toolbox
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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