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Linear eddy viscosity models

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Turbulence modeling
Turbulence
RANS-based turbulence models
  1. Linear eddy viscosity models
    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
      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
      3. Realisability issues
        1. Kato-Launder modification
        2. Durbin's realizability constraint
        3. Yap correction
        4. Realisability and Schwarz' inequality
  2. Nonlinear eddy viscosity models
    1. Explicit nonlinear constitutive relation
      1. Cubic k-epsilon
      2. EARSM
    2. v2-f models
      1. \overline{\upsilon^2}-f model
      2. \zeta-f model
  3. Reynolds stress model (RSM)
Large eddy simulation (LES)
  1. Smagorinsky-Lilly model
  2. Dynamic subgrid-scale model
  3. RNG-LES model
  4. Wall-adapting local eddy-viscosity (WALE) model
  5. Kinetic energy subgrid-scale model
  6. Near-wall treatment for LES models
Detached eddy simulation (DES)
Direct numerical simulation (DNS)
Turbulence near-wall modeling
Turbulence free-stream boundary conditions
  1. Turbulence intensity
  2. Turbulence length scale

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, such as:

 
- \rho \left\langle  u_{i} u_{j} \right\rangle = \mu_{t} \left[ S_{ij} - \frac{1}{3} S_{kk} \delta_{ij} \right]

where \mu_{t} is the coefficient termed turbulence "viscosity" (also called the eddy viscosity), and S_{ij} is the mean strain rate defined by:

 
S_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}} \right]

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 are 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
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