Line term in the Navier - Stokes equation.

vgoy · October 21, 2021, 12:33

Hi!

I am new in fluid dynamics. In my scientific study required to introduce a linear term to the Navier Stokes equation. It means that on the right-hand side I have $-\nabla p-\frac{1}{\tau} U$ , where $\tau$ is constant. I found that OpenFOAM can solve this type of equation. I chose icoFoam solver for it and added line term in the next way:
fvVectorMatrix UEqn
(
fvm::ddt(U)
+ fvm::div(phi, U)
- fvm::laplacian(nu, U)
+ fvm::Sp(tauI, U)
);

Then I did some calculations, it seems to work. The only question left is, did I add the linear term correctly? Can I add it in another way to speed up the calculation? I have been looking for answers to my questions in the Internet for a long time, but for this I need to immerse myself in fluid dynamics with the right textbooks. Can you please tell me if I am on the right path? or a simple mistake?

Many thank for the help!

David* · October 26, 2021, 08:58

The use of fvm::Sp seems correct to me, also the positive sign. But are you really sure that tauI is correct and not 1/tauI?

Regards,
David

Sources:
https://openfoamwiki.net/index.php/H...sport_equation
https://openfoamwiki.net/index.php/IcoFoam

vgoy · October 26, 2021, 09:07

Dear David,

thank you for your answer, this is important to me. Whenever you see an easy solution to your problem, it seems that there is a catch somewhere. For me, tauI is inverse tau, namely tauI=1/tau.

Best regards,
Vova.

October 21, 2021, 12:33	Line term in the Navier - Stokes equation.	#1
vgoy New Member Vladimir Join Date: Oct 2021 Posts: 2 Rep Power: 0	Hi! I am new in fluid dynamics. In my scientific study required to introduce a linear term to the Navier Stokes equation. It means that on the right-hand side I have $-\nabla p-\frac{1}{\tau} U$ , where $\tau$ is constant. I found that OpenFOAM can solve this type of equation. I chose icoFoam solver for it and added line term in the next way: fvVectorMatrix UEqn ( fvm::ddt(U) + fvm::div(phi, U) - fvm::laplacian(nu, U) + fvm::Sp(tauI, U) ); Then I did some calculations, it seems to work. The only question left is, did I add the linear term correctly? Can I add it in another way to speed up the calculation? I have been looking for answers to my questions in the Internet for a long time, but for this I need to immerse myself in fluid dynamics with the right textbooks. Can you please tell me if I am on the right path? or a simple mistake? Many thank for the help!

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October 26, 2021, 08:58		#2
David* Member David GISEN Join Date: Jul 2009 Location: Germany Posts: 68 Rep Power: 16	The use of fvm::Sp seems correct to me, also the positive sign. But are you really sure that tauI is correct and not 1/tauI? Regards, David Sources: https://openfoamwiki.net/index.php/H...sport_equation https://openfoamwiki.net/index.php/IcoFoam

October 26, 2021, 09:07		#3
vgoy New Member Vladimir Join Date: Oct 2021 Posts: 2 Rep Power: 0	Dear David, thank you for your answer, this is important to me. Whenever you see an easy solution to your problem, it seems that there is a catch somewhere. For me, tauI is inverse tau, namely tauI=1/tau. Best regards, Vova.