URANS

Keep the time derivative

URANS advances the averaged variables in physical time. In the incompressible RANS momentum equation this means retaining $\partial(\rho\overline{u_k})/\partial t$, with the Reynolds stresses still closed using a RANS model. An ensemble-mean interpretation allows $\overline{u_k}(\mathbf x,t)$ to vary with time.

What can be resolved

URANS can reproduce some organized, time-dependent phenomena such as imposed pitching or periodic shedding when the closure and setup permit it. It models the turbulence stresses through a RANS closure. A smaller time step improves time discretization of the URANS solution and does not change that closure into a subgrid-scale model.

What to check

• Compare loads, frequencies and phase against data when those outputs matter.
• Repeat at smaller physical time steps and check inner convergence if the time integrator requires it.
• For periodic forcing compare several settled cycles. For time averages, document the averaging window and demonstrate that it is adequate.
• Inspect whether numerical diffusion or eddy viscosity is damping the flow structures of interest.

Sources

• NASA · Temporal convergence in CFD
• NASA NTRS · assessment of URANS and scale-resolving methods for transonic buffet