# Laplacian term in N-S equation

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 July 22, 2011, 11:15 Laplacian term in N-S equation #1 New Member   Diego Villa Join Date: Mar 2010 Location: Genova Italy Posts: 28 Rep Power: 7 Hi All, I have a little question on the Navier-Stokes implementation in OF. In the interPhaseChangeFoam solver the N-S equation has written as: fvVectorMatrix UEqn ( fvm::ddt(rho, U) + fvm::div(rhoPhi, U) - fvm::Sp(fvc::ddt(rho) + fvc::div(rhoPhi), U) - fvm::laplacian(muEff, U) - (fvc::grad(U) & fvc::grad(muEff)) ); My question is: what does the term "- (fvc::grad(U) & fvc::grad(muEff))" mean? In the theory that term shouldn't exist. if it's true the relationship laplacian(muEff, U)=muEff*laplacian(U)+grad(U)*grad(muEff) (see P-38 in Programmers Guide) I make some mistake? Diego

July 25, 2011, 23:26
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Senior Member

Mirko Vukovic
Join Date: Mar 2009
Posts: 159
Rep Power: 8
Quote:
 Originally Posted by DiegoNaval Hi All, I have a little question on the Navier-Stokes implementation in OF. In the interPhaseChangeFoam solver the N-S equation has written as: fvVectorMatrix UEqn ( fvm::ddt(rho, U) + fvm::div(rhoPhi, U) - fvm::Sp(fvc::ddt(rho) + fvc::div(rhoPhi), U) - fvm::laplacian(muEff, U) - (fvc::grad(U) & fvc::grad(muEff)) ); My question is: what does the term "- (fvc::grad(U) & fvc::grad(muEff))" mean? In the theory that term shouldn't exist. if it's true the relationship laplacian(muEff, U)=muEff*laplacian(U)+grad(U)*grad(muEff) (see P-38 in Programmers Guide) I make some mistake? Diego
Could it be that this term is to improve convergence/stability, and that it is zero when the solution is reached?

Mirko

 July 26, 2011, 05:38 #3 New Member   Diego Villa Join Date: Mar 2010 Location: Genova Italy Posts: 28 Rep Power: 7 Hi Mirko I'm not sure of that. Why this terms should be zero when the solution is reached? Both therms are not zero at the end, and why the inner product should be zero? Could you send me a reference about that? Thanks a lot for the replay Diego

 July 26, 2011, 06:25 #4 Senior Member   Pablo Join Date: Mar 2009 Posts: 102 Rep Power: 8 Hi Diego, The answer is here "http://www.cfd-online.com/Forums/openfoam/82640-interfoam-ueqn.html" and here "http://powerlab.fsb.hr/ped/kturbo/OpenFOAM/SummerSchool2009/presentations/MitjaMorgut2009.pdf"

 July 26, 2011, 11:45 #5 New Member   Diego Villa Join Date: Mar 2010 Location: Genova Italy Posts: 28 Rep Power: 7 Hi Pablo I'm agree that if the muEff is not constant the terms "div(muEff*grad(U))" and "muEff*lapalcian(U)" are different, but in the Navie- Stokes equation the first term is the right one. But as the OF Programmers Guide tell at P-38, the openfoam command laplacian(muEff,U), should be intended as the div(muEff*grad(U)) and not asmuEff*lapalcian(U), so should be not necessary split the terms in two contribute in the equation. If I say something wrong...could you say me where? Diego

 July 26, 2011, 14:36 #6 Senior Member   Pablo Join Date: Mar 2009 Posts: 102 Rep Power: 8 Let me known if with this pic it is clear http://imageshack.us/photo/my-images/3/formulasns.jpg

 July 27, 2011, 03:44 #7 Senior Member     Anton Kidess Join Date: May 2009 Location: Delft, Netherlands Posts: 919 Rep Power: 17 Pablo, you have errors in the bracketing of the equations in the three lines of your eqnarray. The final result is correct though

 July 27, 2011, 04:25 #8 New Member   Diego Villa Join Date: Mar 2010 Location: Genova Italy Posts: 28 Rep Power: 7 Thank you very much Pablo, I found the little mistake in the brackets, but now all it is more clear. In every books i found that this therm is always hides in the source terms without explicit its. Thank you again.

 July 27, 2011, 06:56 #9 Senior Member   Pablo Join Date: Mar 2009 Posts: 102 Rep Power: 8 Sorry, brackets are wrong at the stress term. Pablo

 July 20, 2012, 14:32 transpose term #10 Member   ehsan Join Date: Mar 2009 Posts: 92 Rep Power: 8 Dear All I like to ask a question: What happen to the term of transpose of (Grad (U))? To what term it is converted in equation given in "http://imageshack.us/photo/my-images/3/formulasns.jpg/" Regards Ehsan

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