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Transformation of k and eps equations

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Old   March 19, 2001, 09:24
Default Transformation of k and eps equations
Marat Hoshim
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Hi all,

in some papers using the SST k-omega model there's said, that the k and eps equations were transformed into the k and omega formulation. Does someone know a detailed reference, that shows how this transformation is done step by step.

Regards, Marat
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Old   March 20, 2001, 08:07
Default Re: Transformation of k and eps equations
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You might try Menter's paper(s) where he first introduces the SST model. They aren't overly detailed, but they do give the basic way his model combine the k-epsilon and k-omega.

The references are:

Menter, F. R., "Improved Two-Equation k-omega Turbulence Models for Aerodynamic Flows", NASA TM-103975 .

Menter, F. R., "Two Equation Eddy Viscosity Turbulence Models for Engineering Applications", AIAA Journal, Vol. 32, No. 8, August 1994.
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Old   March 20, 2001, 08:46
Default Re: Transformation of k and eps equations
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I don't have any reference, but you should look to papers from Aupoix et al. if there is any.

The main idea is the following :

let phi be any function of k and eps such as :

phi = k^{alpha} * eps^{beta}

it comes :

(1/phi)d(phi)/dt = alpha * (1/k) d(k)/dt + beta * (1/eps)d(eps)/dt

since d(k)/dt and d(eps)/dt are already known, it is possible to write the equation of any kind of phi. The difficulty is then to deal with the cross terms (coming form the viscous term).

hope that helps,


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Old   March 21, 2001, 10:15
Default Re: Transformation of k and eps equations
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I forgot :

omega = eps/k

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Old   March 7, 2011, 09:33
The True
Join Date: Dec 2010
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Eren10 is on a distinguished road
Does someone know how to transform the k-epsilon for the SST model.

I need to know how Menter came to the closure coefficients:

\sigma_{w2} = 0.856 and \beta_2 = 0.0828
Eren10 is offline   Reply With Quote


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