• Two equation model for the turbulence kinetic energy, \(k\), and turbulence specific dissipation rate, \(\omega\).
  • Aims to overcome the defficiencies of the standard k-omega model wrt dependency on the freestream values of k and omega
  • Able to capture flow separation
  • OpenFOAM variant is based on the 2003 model [49]

Model equations

The turbulence specific dissipation rate equation is given by:

\[\Ddt{\rho \omega} = \div \left( \rho D_\omega \grad \omega \right) + \frac{\rho \gamma G}{\nu} - \frac{2}{3} \rho \gamma \omega \left( \div \u \right) - \rho \beta \omega^2 - \rho \left(F_1 - 1\right) CD_{k\omega} + S_\omega,\]

and the turbulence kinetic energy by:

\[\Ddt{\rho k} = \div \left( \rho D_k \grad k \right) + \rho G - \frac{2}{3} \rho k \left( \div \u \right) - \rho \beta^{*} \omega k + S_k.\]

The turbulence viscosity is obtained using:

\[\nu_t = a_1 \frac{k}{\max (a_1 \omega_, b_1 F_{23} \tensor{S})}\]

Default model coefficients

\(\alpha_{k1}\) \(\alpha_{k2}\) \(\alpha_{\omega 1}\) \(\alpha_{\omega 2}\) \(\beta_1\) \(\beta_2\) \(\gamma_1\) \(\gamma_2\)
0.85 1.0 0.5 0.856 0.075 0.0828 5/9 0.44
\(\beta^{*}\) \(a_1\) \(b_1\) \(c_1\)
0.09 0.31 1.0 10.0


For isotropic turbulence, the turbulence kinetic energy can be estimated by:

\[k = \frac{3}{2} \left(I |\u_{\ref}|\right)^{2}\]

where \(I\) is the intensity, and \(\u_{\ref}\) a reference velocity. The turbulence specific dissipation rate follows as:

\[\omega = \frac{k^{0.5}}{C_{\mu}^{0.25} L}\]

where \(C_{\mu}\) is a constant equal to 0.09, and \(L\) a reference length scale.


The model is specified using:

    turbulence      on;
    RASModel        kOmegaSST;

Boundary conditions




  • wall functions

Further information

Source code:


  • Base model: Menter and Esch [48]
  • Updated model: Menter et al. [49]
  • Corrections: consistent production terms from the 2001 paper as form in the 2003 paper is a typo, see [52]
  • F3 term for rough walls: Hellsten [24]

See also: