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Adding implicit source term to momentum equation

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Old   September 18, 2009, 04:31
Default Adding implicit source term to momentum equation
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Dr. Fabian Schlegel
Join Date: Apr 2009
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after spending days in unterstanding the source code and the mathematics of the oodles solver to add a velocity dependend source term to the navier stokes equation I now have a idea but I am not really sure if this is right.
So hopefully somebody could verfify my idea and here it comes:

I want to add the following term to my navier stokes equation on the right hand side: F_i = - cd * a * mag(U) * U
I want to treat this term implicit. After searching the forum and the source code of the other solver it should be possible to do this:

fvVectorMatrix UEqn
(
fvm::ddt(U)
+ fvm::div(phi, U)
+ sgsModel->divDevBeff(U)
+ fvm::Sp(cd*a*mag(U),U)
);
For my understanding OpenFoam will handle U implizit but mag(U) will be explizit? But I is it also possible and reasonable to do something like this:

fvVectorMatrix UEqn
(
fvm::ddt(U)
+ fvm::div(phi, U)
+ sgsModel->divDevBeff(U)
+ fvm::Sp(mag(fmv::Sp(cd*a, U)), U)
);

cd is a scalar and a in the first approach too but in the end it should be a scalar field. So I havent tried this yet it is still theoretical but may be someone could verify my idea :-D

thx

Fabian
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