- **OpenFOAM**
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- - **origin of fvm::Sp(fvc::div(phi_), epsilon_) in kepsilon Eqn?**
(*https://www.cfd-online.com/Forums/openfoam/64602-origin-fvm-sp-fvc-div-phi_-epsilon_-kepsilon-eqn.html*)

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

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 |

Dear Hrv,
Many thanks for the information. I look further into it! Cheers, Bob |

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 |

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 |

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 |

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 |

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