# Turbulence Modeling

AcuSolve supports a variety of turbulence models for fluid flow simulations. For steady state simulations the Reynolds-averaged Navier-Stokes equations are solved to arrive directly at the time averaged flow field. In case of transient simulations the governing equations are integrated in time to yield an accurate description of the flow field. There are also many different turbulence closure methods available for each type of simulation.

The various turbulence models used in AcuSolve are:
One Equation and Two Equation Models
Spalart-Allmaras (SA) turbulence model
Shear Stress Transport (SST) turbulence model
$k-\omega$ turbulence model
$k-\epsilon$ model
RNG $k-\epsilon$ model
Realizable $k-\epsilon$ model
Detached Eddy Simulation (DES) Models
SA – DES
SST – DES
Dynamic DES (DDES)
Large Eddy Simulation (LES) Models
Classical (Smaroginsky) model
Dynamic subgrid LES model

## Turbulence Wall Function

The first option for computing turbulent boundary layers is to fully resolve them. When computing the near wall gradients explicitly, AcuSolve integrates the governing equations directly to the wall. As a result, this option is more accurate, provided that sufficient mesh density is used. ${y}^{+}$ (defined below) of the first mesh point must be less than 10 (preferably 5); otherwise, gross errors in traction, heat flux, and mass transfer may result. This option is typically used for applications where the near wall flow profile plays an important role in the physics of the simulation, that is, cases having adverse pressure gradients, flow separation, and so on. This option is activated by specifying the turbulence_wall_type = low_reynolds_number (or low_re) parameter in the SIMPLE_BOUNDARY_CONDITION command.

${y}^{+}=\frac{\rho y{u}^{*}}{\mu }$

where $\mu$ is the viscosity, ${u}^{*}=\sqrt{\frac{{\tau }_{w}}{\rho }}$ is the turbulent friction velocity, ${\tau }_{w}$ is the wall shear stress, $\rho$ is the density.

The second type of wall treatment for turbulent boundary layers allows you to approximate the near wall flow field, without using fine near wall mesh, by employing wall functions. This approach can greatly reduce the size of a mesh by eliminating the need for fine mesh spacing normal to no-slip walls. When this approach is applied, AcuSolve assumes a shape for the near wall flow field. This assumed profile is based on the “Law of the Wall” for turbulent boundary layers. The “Law of the Wall” is a relation that is based on theoretical and experimental arguments and relates the stream wise velocity profile with the normal distance from the wall. This relation was formulated for fully developed boundary layers with favorable pressure gradients. This option is activated by specifying the turbulence_wall_type = wall_function (or func) parameter in the SIMPLE_BOUNDARY_CONDITION command. ${y}^{+}$ of the first mesh point may be as large as 300.

The third type of wall model that is offered by AcuSolve is the running average wall function. When this model is employed, the wall function is evaluated using the running average velocity field and not the instantaneous field. This approach is typically used with LES and DES models, but may also be used with RANS if appropriate.
Note: This requires the Running Average field to be turned on in the simulation. This option is activated by specifying the turbulence_wall_type = running_average_wall_function parameter in the SIMPLE_BOUNDARY_CONDITION command.