15 Scale-Adaptive Turbulence Extension
Current status. The selectable scale-adaptive option is an extension of the GE \(k-\omega\) carrier model, not a separate carrier-flow family. Source-resident LES helpers are not presented here as a current selectable production model.
15.1 Scale-adaptive source term
The turbulence length scale used by the source is
\[L=\frac{\sqrt{k}}{C_\mu^{1/4}\omega},\qquad C_\mu=0.09.\](15.1)The cell filter length is
\[\Delta=V^{1/3}.\](15.2)CMPS uses the magnitude of the velocity Laplacian,
\[\mathcal U_{\nabla^2}=\|\nabla^2\mathbf u\|_2,\](15.3)to form a von-Karman-like scale. The two candidates are
\[L_{vk,1}=\frac{\kappa S}{\max(\mathcal U_{\nabla^2},\epsilon)},\](15.4)\[L_{vk,2}=C_s\Delta\sqrt{\frac{\kappa\eta_2}{\beta/C_\mu-\alpha}},\](15.5)\[L_{vk}=\max(L_{vk,1},L_{vk,2}).\](15.6)The current constants are \(\kappa=0.41\), \(C_s=0.11\), \(\eta_2=3.51\) and \(\alpha=0.52\).
15.2 Implemented omega-equation SAS production
Let
\[R_\omega=\frac{|\nabla\omega|^2}{\omega^2},\qquad R_k=\frac{|\nabla k|^2}{k^2}.\](15.7)The added nonnegative source is
\[Q_{SAS}=\max\!\left\{\rho\left[\eta_2\kappa S^2\left(\frac{L}{L_{vk}}\right)^2-\frac{2Ck}{\sigma_\phi}\max(R_\omega,R_k)\right],0\right\}.\](15.8)The current constants are \(C=2\) and \(\sigma_\phi=2/3\). This term is added to the omega source group together with \(G_\omega-Y_\omega+D_\omega\).
15.3 Additional derivative requirement
Because \(L_{vk,1}\) depends on \(\|\nabla^2\mathbf u\|\), the SAS path explicitly computes a velocity-Laplacian magnitude in addition to the first primitive gradients used by the base model. This is why the optional SAS path has additional gradient/communication work compared with steady GE-RANS.
15.4 Interpretation and limitations
The source term is clipped at zero, so the scale-adaptive contribution cannot become a negative omega production through this term. Its effectiveness is controlled by the ratio \(L/L_{vk}\) and by the competing normalized \(k\)/\(\omega\) gradient term. The current manual therefore treats SAS as an optional source modification to the GE-RANS equations rather than advertising a separate LES/DES equation set.