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Advice on projection/fractional step methods

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Old   July 4, 2017, 11:21
Default Advice on projection/fractional step methods
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David
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Dear all,

I have a fully coupled unsteady FEM Navier-Stokes code, used in the context of hemodynamics, in particular flow through stenosis with Reynolds numbers of the order of ~2500. (I suspect the flow to be near transition; LES will be carried out later to confirm.)

I'd like to implement projection/fractional step/splitting methods for efficiency. There are many schemes and many names in the game, so I'd like to ask about your experiences and recommendations. What are your favorites?
In particular: implicit or explicit convection? Pressure treatment?

Thanks for your advice!

Regards
David
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Old   July 4, 2017, 12:22
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Filippo Maria Denaro
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I always used the pressure-free projection method... Second order in time using explicit for the convection and the SGS terms and implicit for the diffusion.
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Old   July 4, 2017, 18:09
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Thanks for your comment. Can you elaborate on why you chose pressure-free (e.g. instead of incremental pressure correction)?
Are there any considerations w.r.t. BDF2 vs. Crank-Nicolson?

Thanks
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Old   July 4, 2017, 18:32
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Quote:
Originally Posted by dajuno View Post
Thanks for your comment. Can you elaborate on why you chose pressure-free (e.g. instead of incremental pressure correction)?
Are there any considerations w.r.t. BDF2 vs. Crank-Nicolson?

Thanks

In general, when well-formulated, these fractional methods are all quite good. A detailed analysis of each method does not lead to a definition of the "best one". I can say that each method produces a different meaning of the "pressure" field.

Then, BDF2 vs. Crank-Nicolson is something related only to the solution of the intermediate momentum equation. The CN scheme produces a stable solution and allows to work with reasonable time-step. The intermediate velocity must be prescribed at the boundary and this is, however, an issue to consider carefully. The BDF2 I used (Adams-Bashforth) is stable provided that the time-step is constrained by the (cfl-Re_h) stability region.

You can find a lot of published literature about that.
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