A very simple one-equation model has been developed by Menter [32] [33]. It is derived directly from the model and is therefore named the model:

(2–79)

where is the kinematic eddy viscosity, is the turbulent kinematic eddy viscosity and is a model constant.

The model contains a destruction term, which accounts for the structure of turbulence and is based on the von Karman length scale:

(2–80)

where S is the shear strain rate tensor. The eddy viscosity is computed from:

(2–81)

In order to prevent a singularity of the formulation as the von Karman length scale goes to zero, the destruction term is reformulated as follows:

(2–82)

(2–83)

The coefficients are:

By default, the model is solved in combination with the scalable wall function. For details, see Scalable Wall Functions.

 

2.2.3.1. Low Reynolds Number Formulation

Low Reynolds formulation of the model is obtained by including damping functions. Near wall damping functions have been developed to enable integration to the surface:

(2–84)

where D ₂ is required to compute the eddy-viscosity that goes into the momentum equations:

(2–85)

The low Reynolds formulation of the model requires a near wall mesh resolution of .