### 2.2.3. The Eddy Viscosity Transport Model

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:

Coefficient | Value
--- | ---
c 1 | 0.144
c 2 | 1.86
c 3 | 7.0
A + | 13.5
| 0.41
| 1.0

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 .

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