# Linear eddy viscosity models

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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]]. | ||

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+ | 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. | ||

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+ | # [[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:

where is the coefficient termed turbulence "viscosity" (also called the eddy viscosity), and is the *mean* strain rate defined by:

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.