SST k-equation production and dissipation

Two-equation SST models share a pure production/dissipation kernel for the turbulent kinetic energy equation.

Production variants

  • Boussinesq (full): \(P_k = \mu_t(S_{ij}:S_{ij}-\tfrac23(\nabla\cdot\mathbf{v})^2)/Re - \tfrac23\rho k\nabla\cdot\mathbf{v}\)

  • SST-2003 strain-only: \(P_k = \mu_t S_{ij}:S_{ij}/Re\)

  • SST-V vorticity: replace \(S:S\) by vorticity magnitude squared.

Dissipation

\[\varepsilon = f_{\beta^*}\beta^*\rho k\omega\]

or DES form \(f_{\beta^*}\rho k^{3/2}/L\). Production is limited by \(P_k \leftarrow \min(P_k,\, p_{k,\mathrm{lim}}\varepsilon)\).

References

  • Menter, F. R. Two-equation eddy-viscosity turbulence models for engineering applications (SST).

  • NASA Turbulence Modeling Resource — SST (https://turbmodels.larc.nasa.gov/sst.html).

  • See sa_source.rst and references.rst for the citation / intermediate-verification policy.

Pure APIs: TurbSstPolicy.h. Tests: turb_sst_policy_test.

Residual assembly and diagonals

Related pure pieces (also used for the omega equation):

\[S_k = P_k - \varepsilon,\qquad S_\omega = P_\omega - D_\omega + CD\]
\[d_k = -2 f_{\beta^*}\beta^*\omega,\qquad d_\omega = -2 f_\beta\beta\omega - \frac{|CD|}{\rho\omega}\]

Locks: turb_sst_residual_test (including SstDiagonalW). Contract Workbench entry: sst_residual_diagonal.