Turbulence scalar convective upwind flux

Turbulence working variables (SA \(\tilde\nu\), SST \(k,\omega\), …) use a face-normal upwind convective flux with optional density weighting.

Relative normal velocity

\[v_n = \mathbf{n}\cdot\mathbf{v} - v_{fn}\]

Split

\[v_n^+ = \tfrac12(v_n+|v_n|),\qquad v_n^- = \tfrac12(v_n-|v_n|)\]

Density weight

\[w = \alpha + (1-\alpha)\rho\]

with \(\alpha=1\) for SA (flux of \(\tilde\nu\)) and \(\alpha=0\) for density-weighted two-equation models.

Scalar flux

\[F = (v_n^+ w_L)\phi_L + (v_n^- w_R)\phi_R\]

References

• Spalart, P. R. and Allmaras, S. R. A one-equation turbulence model.

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

• See references.rst.

Pure APIs: TurbInvFluxPolicy.h. Tests: turb_inv_flux_policy_test.