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July 23, 2013, 19:12 
Extra terms in turbulence model transport equations

#1 
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Hi,
I have been working on rewriting some parts of the kOmegaSST turbulence model, and recently realised there are some 'extra' terms in the transport equations for k and omega, notably  for omega: Code:
tmp<fvScalarMatrix> omegaEqn ( fvm::ddt(omega_) + fvm::div(phi_, omega_)  fvm::Sp(fvc::div(phi_), omega_)  fvm::laplacian(DomegaEff(F1), omega_) == gamma(F1)/nut_*min(G, c1_*betaStar()*k_*omega_)  fvm::Sp(beta(F1)*omega_, omega_)  fvm::SuSp ( (F1  scalar(1))*CDkOmega/omega_, omega_ ) ); Code:
tmp<fvScalarMatrix> kEqn ( fvm::ddt(k_) + fvm::div(phi_, k_)  fvm::Sp(fvc::div(phi_), k_)  fvm::laplacian(DkEff(F1), k_) == min(G, c1_*betaStar()*k_*omega_)  fvm::Sp(betaStar()*omega_, k_) ); I have been using a combination of references, but these do not appear in any of them, so they must be an openFoam programming peculiarity. Does anyone know / could anyone explain where these terms come from / why we have them in the eqns? thanks very much in advance much appreciated jonathan 

July 23, 2013, 20:59 

#2 
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Daniel P. Combest
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Location: St. Louis, USA
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This has been discussed in several places
But it is one of my favorite things in fluid mechanics for some reason . The definition of the advection operator is where the left side is the conservative form and the right side is the primitive form ( according to anishtain4 from gas dynamics lingo). The use if this term Code:
 fvm::Sp(fvc::div(phi_), k_) Code:
fvm::SuSp(fvc::div(phi_),k_) Code:
fvc::div(phi_) EDIT: There is actually a little bit of a discussion in "Computational Methods for Fluid Dynamics" by Ferziger and Peric' (3rd edition) on page 162 referring to the conservation of the kinetic energy equation. Last edited by chegdan; August 22, 2013 at 16:37. Reason: Added more information and a literature source and forgot a dot product 

August 14, 2013, 09:24 

#3  
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Hi Daniel,
apologies for the slow reply here  i saw your post and it helped a lot, however, things have been quite hectic this side, hence the late thanks. again, thanks for your help  much appreciated jonathan Quote:


August 19, 2013, 11:01 

#4 
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Daniel P. Combest
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No worries, I enjoy discussing this topic. If anyone else has some thoughts that could expand this information I would love to hear about it. I can always learn more on the topic!


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