# Linear eddy viscosity models

(Difference between revisions)
 Revision as of 17:17, 30 October 2009 (view source)← Older edit Revision as of 17:26, 30 October 2009 (view source)Newer edit → Line 14: Line 14: 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]]. 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. + + # [[Algebraic turbulence models|Algebraic models]] + ##[[Cebeci-Smith model]] + ##[[Baldwin-Lomax model]] + ## [[Johnson-King model]] + ## [[A roughness-dependent model]] + # [[One equation turbulence models|One equation models]] + ## [[Prandtl's one-equation model]] + ## [[Baldwin-Barth model]] + ## [[Spalart-Allmaras model]] + # [[Two equation models]] + ## [[k-epsilon models]] + ### [[Standard k-epsilon model]] + ### [[Realisable k-epsilon model]] + ### [[RNG k-epsilon model]] + ### [[Near-wall treatment for k-epsilon models]] + ## [[k-omega models]] + ### [[Wilcox's k-omega model]] + ### [[Wilcox's modified k-omega model]] + ### [[SST k-omega model]] + ### [[Near-wall treatment for k-omega models]] + ## [[Two equation turbulence model constraints and limiters]] + ### [[Kato-Launder modification]] + ### [[Durbin's realizability constraint]] + ### [[Yap correction]] + ### [[Realisability and Schwarz' inequality]] + [[Category:Turbulence models]] [[Category:Turbulence models]]

## Revision as of 17:26, 30 October 2009

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.