For LES models, the velocity scales are estimated based on an eddy viscosity and LES grid length scale :

(4–455)

(4–456)

The time scales and are defined in the following way

(4–457)

(4–458)

The definition of the LES grid length scale depends on the specified model. Using the Smagorinsky-Lilly, WALE, or one of the Algebraic Wall-Modeled LES models, it is computed as:

(4–459)

where is the von Kármán constant, is the distance to the closest wall, a model coefficient, and represents the local grid scale based on the cell volume (as shown in the following equation).

(4–460)

Note that WMLES uses a more complex formulation of in the definition of the eddy viscosity (see Algebraic WMLES Model Formulation for more details).

In dynamic LES models (that is, the dynamic Smagorinsky-Lilly model and the dynamic kinetic energy subgrid-scale model), the LES grid length scale is estimated based on the dynamic procedure.