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Convectional term fvm::Sp(fvc::div(phi_), epsilon_) in RNGkEpsilon OF 1.7.1 missing 

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May 25, 2011, 11:56 
Convectional term fvm::Sp(fvc::div(phi_), epsilon_) in RNGkEpsilon OF 1.7.1 missing

#1 
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Hi!
I have a quistion: why this terms are missing in RNGkEpsilon model in epsilon and k equations? Code:
fvm::ddt(epsilon_) + fvm::div(phi_, epsilon_)  fvm::Sp(fvc::div(phi_), epsilon_)  fvm::laplacian(DepsilonEff(), epsilon_) ... fvm::ddt(k_) + fvm::div(phi_, k_)  fvm::Sp(fvc::div(phi_), k_)  fvm::laplacian(DkEff(), k_) the Code:
+ fvm::SuSp(fvc::div(phi_), epsilon_) ... + fvm::SuSp(fvc::div(phi_), k_) Only one remark: why there is no such treatment for kEpsilon model in OF1.6ext (in kEpsilon.C)? BTW the residuals normalization used now in OF is not appropriated, because it is connected with the source term and for the turbulent transport equations produces underestimated residuals level. Regards, Alexander
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben http://smmp.unileoben.ac.at 

May 26, 2011, 02:35 

#2  
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Alberto Passalacqua
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Quote:
It seems you are trying to treat the convective term in nonconservative form (why?). If you think to: div(kU) = U . grad(k) + k div(U), you are discretizing U . grad(k), since you have the full convective term in conservative form at the line fvm::div(phi_, epsilon_) Best,
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Alberto Passalacqua GeekoCFD  A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as in both physical and virtual formats (current status: http://albertopassalacqua.com/?p=1541) OpenQBMM  An opensource implementation of quadraturebased moment methods. To obtain more accurate answers, please specify the version of OpenFOAM you are using. Last edited by alberto; May 26, 2011 at 10:08. 

May 26, 2011, 05:14 

#3 
Senior Member

... I ask because IT IS, for example, in realizableKE (incompressible) in OF 1.7.1:
Code:
// Dissipation equation tmp<fvScalarMatrix> epsEqn ( fvm::ddt(epsilon_) + fvm::div(phi_, epsilon_)  fvm::Sp(fvc::div(phi_), epsilon_)  fvm::laplacian(DepsilonEff(), epsilon_) == C1*magS*epsilon_  fvm::Sp ( C2_*epsilon_/(k_ + sqrt(nu()*epsilon_)), epsilon_ ) ); ... // Turbulent kinetic energy equation tmp<fvScalarMatrix> kEqn ( fvm::ddt(k_) + fvm::div(phi_, k_)  fvm::Sp(fvc::div(phi_), k_)  fvm::laplacian(DkEff(), k_) == G  fvm::Sp(epsilon_/k_, k_) ); Heh..., it is funny, the flux phi is divergence free... So why is it included? div(UK) k = U grad(k) + k div(U) = U grad(k) for incompressible liquid. That is well known transition between conservative and nonconservatives forms of the convectional term. Alberto, I am sorry, but would you be kind to clarify: is convectional term in RNG somehow different from those in standard and realizable kepsilon? And are you tallking about 1.7.x, which is not 1.7.1? Do you mean some development version?
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben http://smmp.unileoben.ac.at 

May 26, 2011, 05:36 

#4 
Senior Member

So I agree with Alberto,
that U*grad(k) or U*grad(epsilon) or U*grad(omega) are discretized. Hmm..., why? Is it some error? For example, standard kepsilon, transport of kinetic energy is: dk/dt + div(U K) = div(D_k grad(k)) + G  epsilon There is no terms, from which we can get U*grad(k). Any comments? To avoid missunderstanding: I am not trying to put "div(U*k)  k*div(U) = U*grad(k)" in the OF source code, it is all already there))) I only noticed the difference between approaches how convectional term is discretized in RNGkEpsilon.C and in other incompressible RAS models. I recognized it while modifying RAS models for my solidification part.
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben http://smmp.unileoben.ac.at Last edited by makaveli_lcf; May 26, 2011 at 09:49. Reason: To clarify the question. 

May 26, 2011, 10:15 

#5  
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Alberto Passalacqua
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Hi,
Quote:
As a consequence, they are implementing U . grad(k) = div(U, k)  k div(U), to avoid using U & grad(k), and use the conservative flux. What is not clear to me is why not implementing directly div(phi, k), as in the original equation from the literature?
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May 26, 2011, 11:04 

#6 
Senior Member

Sometimes for the discretization (e.g. for the finite differences method) it is easier to use nonconservative form of the convectional term
div(U*k) = k*div(U)+U & grad(k) But here we get the wrong term. So I will try direct conservative form and compare the results.
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben http://smmp.unileoben.ac.at 

May 26, 2011, 11:25 

#7  
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Alberto Passalacqua
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Quote:
Quote:
div(U*k) = U & grad(k) if div(U) = 0. Now, since numerically it is not exactly zero, they probably enforce the "incompressible form" by using the term U & grad(k) = div(U*k)  k*div(U) This in OpenFOAM becomes fmv::div(phi, k)  fvm::Sp(fvc::div(phi), k), since using phi and not U does not introduce errors, being phi corrected to enforce conservation after solving for p.
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Alberto Passalacqua GeekoCFD  A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as in both physical and virtual formats (current status: http://albertopassalacqua.com/?p=1541) OpenQBMM  An opensource implementation of quadraturebased moment methods. To obtain more accurate answers, please specify the version of OpenFOAM you are using. Last edited by alberto; May 26, 2011 at 11:28. Reason: typo and note 

May 26, 2011, 16:14 

#8 
Senior Member

Alberto, thanks! I got it:
Code:
U = U* + delta U* = U  delta U*  exact solution, delta  error vector div(U*) = 0 (1) div(U) = div(U*) + div(delta) = div(delta) (2) Code:
div(U*.k) = U*&grad(k) Code:
Err1 = div(U.k)  U*&grad(k) = k.div(U*) + U*&grad(k) + k.div(delta) + delta&grad(k)  U*&grad(k) Code:
Err1 = k.div(delta) + delta&grad(k) = k.div(U) + delta&grad(k) div(U.k)  k.div(U) we reduce the calculation error to the delta&grad(k) ))) I am curious, does it worth to use such approach for other scalar equations? E.g. for heat transfer... It would be really nice to here some comment from developers, why they decided to use this method for the turbulence modeling?
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben http://smmp.unileoben.ac.at 

July 19, 2012, 11:53 

#9 
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Daniel WEI (老魏)
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I have the same questions, I feel very confused:
1. Is using "fvm::SuSp(fvc::div(phi_), epsilon_)" better using " fvm::Sp(fvc::div(phi_), epsilon_)"? 2. For other transport equations, should we use this approach? Why it is commented out from RNG kepsilon?
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July 20, 2012, 03:24 

#10 
Senior Member

Hi Daniel!
1. Using SuSp operator is to increase matrix diagonal influence. With Sp operator it goes always to the diagonal and can reduce diagonal elements which makes its solution more problematic for the linear solver. 2. If you check OpenFOAMext such approach is used in all RANS model (*reffering to the source code.... yap! it's there!). I am just using it for RANS models and for energy equation as well. But I did not make any test if it is better for the scalar equation in general. Let's do it! What are your suggestions for the benchmark? It should be some simple case...
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Best regards, Dr. Alexander VAKHRUSHEV Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics" Simulation and Modelling of Metallurgical Processes Department of Metallurgy University of Leoben http://smmp.unileoben.ac.at 

July 20, 2012, 11:06 

#12 
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Daniel WEI (老魏)
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Hmm, Two more questions,
1. When to use source term explicitly and when shall one use it implicitly using Sp or Susp? 2. In ke formulation, why epsilon is solved first instead of k? Thanks
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~ Daniel WEI  Boeing Research & Technology  China Beijing, China 

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