[dajuno]

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

[FMDenaro]

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.

[dajuno]

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

[FMDenaro]

Originally Posted by dajuno

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.