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Solving the poisson equation on collocated grids

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Old   June 16, 2010, 08:43
Question Solving the poisson equation on collocated grids
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Hi,
Does anyone know of any references that shos how to use the SIMPLE method or any other methods to solve the pressure equation (Poisson equation) on collocated grids?
Thanks!
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Old   June 16, 2010, 18:18
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I am not exactly sure what you are after. You could have a look at:

http://www.cfd-online.com/Books/show_book.php?book_id=4

I believe that the book has a good explanation on the simple method and probably some explanation on solvers for the pressure equation.

If you are working in finite volume form and use collocated grids, you will likely need a stabilisation term.

Best of luck.
Julien
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Old   June 16, 2010, 18:49
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Try these books:

Fletecher - Computational Techniques for Fluid Dynamics (vol II)
H. Versteeg, W. Malalasekra - An Introduction to Computational Fluid Dynamics

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Old   June 21, 2010, 06:40
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Thank you for your replies.
Unfortunately I dont have access to the Fletcher book but I've checked the other two.

I have a discretized momentum equation (I used Crank-Nicolson for time and central differencing and 1st order upwind for space discretization) .
Am I correct in saying that Ferziger and Peric mentions that whatever discretization method's used for the momentum equation needs to be applied to the poisson equation too?

Also am I corerct in saying that the SIMPLE method needs to be used for both the pressure and the momentum equations?

Many Thanks
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Old   June 29, 2010, 12:27
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Dear Hooman,

'Am I correct in saying that Ferziger and Peric mentions that whatever discretization method's used for the momentum equation needs to be applied to the poisson equation too?'

Yes. Poisson equation come from the pressure correction formula which is come from your discretization.

'Also am I corerct in saying that the SIMPLE method needs to be used for both the pressure and the momentum equations?'

Yes. Actually SIMPLE stand for semi-implicit method for pressure-linked equations. It's not only for pressure, it's for velocities too. There are certain steps to apply this method. You can find it in any CFD books which is discussing about SIMPLE.
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