In general, when the turbulence kinetic energy is needed for modeling a specific term, it is obtained by taking the trace of the Reynolds stress tensor:

(4–253)

As described in Wall Boundary Conditions, an option for the Reynolds stress models based on the -equation is available in Ansys Fluent to solve a transport equation for the turbulence kinetic energy in order to obtain boundary conditions for the Reynolds stresses. In this case, the following model equation is used:

(4–254)

where and is a user-defined source term. Equation 4–254 is obtainable by contracting the modeled equation for the Reynolds stresses (Equation 4–226). As one might expect, it is essentially identical to Equation 4–39 used in the standard - model.

Although Equation 4–254 is solved, the values of obtained are used only for boundary conditions. In every other case, is obtained from Equation 4–253. This is a minor point, however, since the values of obtained with either method should be very similar.