Re: [ff3d-users] Force in a pressure-driven Stokes flow

[Stephane Del Pino]

Dear Benoît.

First, it seems that in FreeFem++, you are solving a potential flow. Did you 
succeed with ff3d doing the same?

Second, since ff3d's discretization is based on a Q1-Q1 element 
(velocity-pressure), it needs to be stabilized with a 'penalty' term (eps in 
this case). The pressure solution depends a lot on the choice of this term.
ff3d does not support Q2-Q1 coupled discretization yet. But, you can already 
use a projection algorithm to do so. I can send you an example of such a 
scheme which provides much better solution than the direct resolution.
I am quite busy now but I can send you the example by the end of the week. 
Remind me if I forget.

Concerning the second way of approximating the force, it requires that the 
null velocity is imposed weakly using a volume penalty (in your case, you 
used a strong formulation --- elimination --- for Dirichlet on the cylinder). 
If I remember, this is described in this paper:
        http://www.math.u-psud.fr/~maury/Files/OP60DelpinoMaury.pdf
If not, you can check B. Maury's web page, you should find an answer.

I hope this gives you enlightenment...

Best regards,
Stéphane.