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Horus April 9, 2013 13:37

omegaWallFunction implementation

I'm studying the implementation of the incompressible omegaWallFunction.


00207        scalar omegaVis = 6.0*nuw[faceI]/(beta1_*sqr(y[faceI]));
00209        scalar omegaLog = sqrt(k[faceCellI])/(Cmu25*kappa_*y[faceI]);
00211        omega[faceCellI] = sqrt(sqr(omegaVis) + sqr(omegaLog));

\omega = \sqrt{\omega_{vis}^2 + \omega_{log}^2}
\omega_{vis} = \frac{6 \nu}{\beta_1 \cdot y^2}
\omega_{log} = \frac{k}{\sqrt[4]{C_\mu} \cdot \kappa \cdot y}

This clearly becomes oo when y approaches 0. Does this account for the turbulence damping near the wall?

Next question: What is G?


00173    volScalarField& G =
00174        const_cast<volScalarField&>
00175        (
00176            db().lookupObject<volScalarField>
00177            (
00178                turbulence.type() + ".G"
00179            )
00180        );

And set here:


00213        G[faceCellI] =
00214            (nutw[faceI] + nuw[faceI])
00215            *magGradUw[faceI]
00216            *Cmu25*sqrt(k[faceCellI])
00217            /(kappa_*y[faceI]);
00218    }

The paper mentioned in the source code is available nowhere...

I'm especially clueless that the last part with the G is about?


fumiya April 9, 2013 18:08

Hi Florian,

For the second question, the followings will be of help:
The term G is the production of turbulent kinetic energy.

Hope this helps,

dancfd April 28, 2014 21:10

Hello all,

I noticed that the logarithmic component of omega1 in the code is not representative of the Menter 2001 paper.

The code is:

scalar omegaLog = sqrt(k[faceCellI])/(Cmu25*kappa_*y[faceI]);
Which gives:
\omega_{log} = \frac{\sqrt{k}}{\sqrt[4]{C_\mu} \kappa y}

Menter 2001 gives:
\omega_{log} = \frac{u_\tau}{\sqrt[4]{C_\mu} \kappa y}
Where C_mu = 0.09.

Why the difference? A message above makes reference to the following website:

The last term of the last equation in the "Standard Wall Functions" section at that link matches the code, but it is still not clear why the code chose the equation that was selected (Wilcox 1994 eq 6.84) and not that which was defined in Menter 2001.

Does anyone know why the code is what it is, and not in line with Menter 2001?



mooby September 21, 2015 05:54

Implementation of SST Wall Function (Menter)

I am also wondering why is there difference between Menter Wall function definition and OF wall function definition. do you have an answer now ??

Blanco September 23, 2015 08:05


do you have the Menter 2001 paper? I'm not able to find it anywhere...but all my references and docs are citing the

\omega_{log} = \frac{\sqrt{k}}{\sqrt[4]{C_\mu} \cdot \kappa \cdot y}

which is what is implemented in OF (correctly IMHO).

Best regards,


mooby September 23, 2015 08:59

Menter 2001 Paper
Hello Andrea,

Unfortunately I also dont hv Menter 2001 Paper. Nevertheless, I have requested someone on CFD online. He hopefully will share it with me. If I receive it, will surely share it with you :)

Blanco September 23, 2015 09:41

Ok thanks,

because I'm wondering if dancfd was correctly citing Menter formula in his post... I mean, if instead of dancfd cited formula which is

\omega_{log} = \frac{u_\tau}{\sqrt[4]{C_\mu} \kappa y}

we have

\omega_{log} = \frac{u_\tau}{\sqrt{C_\mu} \kappa y}

then everything is solved because we know that

\omega_{log} = \frac{u_\tau}{\sqrt{C_\mu} \kappa y} = \frac{\sqrt{k}}{\sqrt[4]{C_\mu} \cdot \kappa \cdot y}

Let's see if someone could provide Menter paper to check.

Best regards,


dancfd September 23, 2015 21:08


The COBEM paper is available in the public domain here: -> just go to Lectures link

It was posted by someone else in this thread, #43:

It looks like you are correct, there must have been an error in my post above because sqrt(Cmu = 0.09) = 0.3 and then everything matches up (if it is Cmu^1/2 instead of ^1/4). Apologies for the confusion caused by this error.


mooby September 24, 2015 01:59

Menter 2001 Paper
Hello Andrea,

Daniel "Dancfd" have sent me the Esh & Menter Paper. If you wish I can forward it to you or you can request Daniel for it :)

Blanco September 24, 2015 02:59

Thanks a lot Daniel and Ali,

so everything is ok now, we can say OF is correct! ;)

Best regards,


mooby September 29, 2015 08:52

Smoothing Function for Friction Velocity
Hi Adrea/Daniel,

I was wondering the Omega_Log term is defined by Menter as

Omega_Log = U_tau/(0.3*kappa*y)

where U_tau is calculated from U_Vis = U1/y & U_Log = U1/((ln(y)/k)+c)

U_Tau = ( (u_Vis)^4 + (U_Log)^4)^(1/4)

But in OF omega_Log is approximated by I think Spalding assumption

i.e. U_Tau = cmu^(1/4)*sqrt(k)

So, what if Menter U_Tau is used in omegaWallFunction .. will that improve the results i.e. mesh independence

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