Turbulence models

Several turbulence models are available. The first one is the mixing length turbulence model of Michel. It gives an expression of the turbulent viscosity as a function of a mixing length depending on the local distance from the wall and on the boundary layer thickness.

The second one is the one-equation model of Spalart-Allmaras (Spalart et al., 1992). In this case, one transport equation for the kinematic turbulent viscosity v is added to the set of mean fbw equations. Several algorithms may be used, with either strong or weak coupling between mean flow and turbulent equations at each time step.

The third model is the Launder-Sharma ke two-equation model. Using this model, the mean flow equations are closed by two additional equations for the turbulence kinetic energy and for its dissipation rate. Low-Reynolds number corrective terms are used.

The time-step is adapted to ensure the stability of the conservative turbulent equations. Numerical 2nd and 4th order viscosity terms are added as well as limiting functions for the turbulent variables.

In the following numerical validations, only the Spalart-Allmaras model will be considered.