Linear eddy viscosity models

From CFD-Wiki

These are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier-Stokes equations, are modelled by a linear constitutive relationship with the mean flow straining field, as:

where

• is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
• is the mean turbulent kinetic energy
• is the mean strain rate

Note that that inclusion of in the linear constitutive relation is required by tensorial algebra purposes when solving for two-equation turbulence models (or any other turbulence model that solves a transport equations for .

This linear relationship is also known as the Boussinesq hypothesis. For a deep discussion on this linear constitutive relationship, check section Introduction to turbulence/Reynolds averaged equations.

There are several subcategories for the linear eddy-viscosity models, depending on the number of (transport) equations solved for to compute the eddy viscosity coefficient.

1. Algebraic models
   1. Cebeci-Smith model
   2. Baldwin-Lomax model
   3. Johnson-King model
   4. A roughness-dependent model
2. One equation models
   1. Prandtl's one-equation model
   2. Baldwin-Barth model
   3. Spalart-Allmaras model
3. Two equation models
   1. k-epsilon models
      1. Standard k-epsilon model
      2. Realisable k-epsilon model
      3. RNG k-epsilon model
      4. Near-wall treatment for k-epsilon models
   2. k-omega models
      1. Wilcox's k-omega model
      2. Wilcox's modified k-omega model
      3. SST k-omega model
      4. Near-wall treatment for k-omega models
   3. Two equation turbulence model constraints and limiters
      1. Kato-Launder modification
      2. Durbin's realizability constraint
      3. Yap correction
      4. Realisability and Schwarz' inequality