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Laplacian term in N-S equation

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Old   July 22, 2011, 11:15
Default Laplacian term in N-S equation
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Diego Villa
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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
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Old   July 25, 2011, 23:26
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Mirko Vukovic
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Quote:
Originally Posted by DiegoNaval View Post
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
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Old   July 26, 2011, 05:38
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Diego Villa
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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
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Old   July 26, 2011, 06:25
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Pablo
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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"
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Old   July 26, 2011, 11:45
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Diego Villa
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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
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Old   July 26, 2011, 14:36
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Pablo
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Let me known if with this pic it is clear

http://imageshack.us/photo/my-images/3/formulasns.jpg
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Old   July 27, 2011, 03:44
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Anton Kidess
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Pablo, you have errors in the bracketing of the equations in the three lines of your eqnarray. The final result is correct though
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Old   July 27, 2011, 04:25
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Diego Villa
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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.
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Old   July 27, 2011, 06:56
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Sorry, brackets are wrong at the stress term.

Pablo
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Old   July 20, 2012, 14:32
Default transpose term
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ehsan
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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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