origin of fvm::Sp(fvc::div(phi_), epsilon_) in kepsilon Eqn?

Bob · May 15, 2009, 18:55

Dear all,

I am trying to figure out what some terms are in the kepsilon turbulence equations, i.e.

- fvm::Sp(fvc::div(phi_), epsilon_)

Does someone know and can tell me where it originates from?
A similar term can be seen in the equation for kinetic energy.

Further on, I was wondering how the continuity equation is accounted for with respect to incompressible flows. I cannot find it in e.g. icoFoam.C. Is it somewhere integrated?

Many thanks in advance!

Regards,
Bob

hjasak · May 16, 2009, 03:11

The term you refer to is added to account for boundedness of k when the model is used with simpleFoam (and alike) and partial convergence of the pressure equation. In other cases, div(flux) will be zero, so the term disappears.

Regarding icoFoam, continuity equation is the pressure equation. Have a look at my Thesis or CFD lecture notes - the full explanation is done in about 2 pages.

Enjoy,

Hrv

Bob · May 18, 2009, 16:16

Dear Hrv,

Many thanks for the information. I look further into it!

Cheers,
Bob

Bob · May 25, 2009, 16:49

Dear Hrvoje,

I am still trying to figure out the term:

- fvm::Sp(fvc::div(phi_), epsilon_)

You mentioned that it is included in the equations to account for boundedness of k, epsilon, or the density (in case of compressible fluids). Do you perhaps have a reference where this is further explained so I can figure out the origin of the term?

Many thanks.

Regards,
Bob

hjasak · May 26, 2009, 18:35

So:

div(phi, epsilon) - in translation: div(U epsilon)

will be bounded only if div(phi) - in translation div(U)) is zero, right?

On the other hand,

U & grad epsilon

is bounded irrespective of the velocity distribution. Thus, on incomplete convergence, we prefer to solve a weak form of convection (U & grad epsilon) rather than the strong form.

Final step:

div(U epsilon) = U & grad epsilon - epsilon div(U).

Clear?

Hrv

Bob · May 29, 2009, 11:07

Dear Hrvoje,

Thanks for the explanations, but I thought the identity of your final step would be written as something like:

div(U epsilon) = U & grad epsilon + epsilon div(U).

Is there some mistake from my side?

Cheers,
Bob

idefix · July 2, 2014, 03:02

Hello
I know this thread is older, but if there is someone interested:
here is an explanation for the question:
http://www.cfd-online.com/Forums/ope...1-missing.html

May 15, 2009, 18:55	origin of fvm::Sp(fvc::div(phi_), epsilon_) in kepsilon Eqn?	#1
Bob New Member Bob De Clercq Join Date: Apr 2009 Location: Belgium Posts: 17 Rep Power: 17	Dear all, I am trying to figure out what some terms are in the kepsilon turbulence equations, i.e. - fvm::Sp(fvc::div(phi_), epsilon_) Does someone know and can tell me where it originates from? A similar term can be seen in the equation for kinetic energy. Further on, I was wondering how the continuity equation is accounted for with respect to incompressible flows. I cannot find it in e.g. icoFoam.C. Is it somewhere integrated? Many thanks in advance! Regards, Bob

May 16, 2009, 03:11		#2
hjasak Senior Member Hrvoje Jasak Join Date: Mar 2009 Location: London, England Posts: 1,907 Rep Power: 33	The term you refer to is added to account for boundedness of k when the model is used with simpleFoam (and alike) and partial convergence of the pressure equation. In other cases, div(flux) will be zero, so the term disappears. Regarding icoFoam, continuity equation is the pressure equation. Have a look at my Thesis or CFD lecture notes - the full explanation is done in about 2 pages. Enjoy, Hrv DheepanPillai, MaLa and randolph like this. __________________ Hrvoje Jasak Providing commercial FOAM/OpenFOAM and CFD Consulting: http://wikki.co.uk

May 26, 2009, 18:35		#5
hjasak Senior Member Hrvoje Jasak Join Date: Mar 2009 Location: London, England Posts: 1,907 Rep Power: 33	So: div(phi, epsilon) - in translation: div(U epsilon) will be bounded only if div(phi) - in translation div(U)) is zero, right? On the other hand, U & grad epsilon is bounded irrespective of the velocity distribution. Thus, on incomplete convergence, we prefer to solve a weak form of convection (U & grad epsilon) rather than the strong form. Final step: div(U epsilon) = U & grad epsilon - epsilon div(U). Clear? Hrv randolph likes this. __________________ Hrvoje Jasak Providing commercial FOAM/OpenFOAM and CFD Consulting: http://wikki.co.uk

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May 18, 2009, 16:16		#3
Bob New Member Bob De Clercq Join Date: Apr 2009 Location: Belgium Posts: 17 Rep Power: 17	Dear Hrv, Many thanks for the information. I look further into it! Cheers, Bob

May 25, 2009, 16:49		#4
Bob New Member Bob De Clercq Join Date: Apr 2009 Location: Belgium Posts: 17 Rep Power: 17	Dear Hrvoje, I am still trying to figure out the term: - fvm::Sp(fvc::div(phi_), epsilon_) You mentioned that it is included in the equations to account for boundedness of k, epsilon, or the density (in case of compressible fluids). Do you perhaps have a reference where this is further explained so I can figure out the origin of the term? Many thanks. Regards, Bob

May 29, 2009, 11:07		#6
Bob New Member Bob De Clercq Join Date: Apr 2009 Location: Belgium Posts: 17 Rep Power: 17	Dear Hrvoje, Thanks for the explanations, but I thought the identity of your final step would be written as something like: div(U epsilon) = U & grad epsilon + epsilon div(U). Is there some mistake from my side? Cheers, Bob

July 2, 2014, 03:02		#7
idefix Member Join Date: Aug 2011 Posts: 89 Rep Power: 15	Hello I know this thread is older, but if there is someone interested: here is an explanation for the question: http://www.cfd-online.com/Forums/ope...1-missing.html