No-penetration_bounadry_condition

1

Hello,

I have a question about the no-penetration boundary condition, how could we implement this condition with say the Taylor-Hood element?

Thanks!

2

If the ‘no-penetration condition’ that you meant is no penetration velocity but the wall is slip wall then this can be implemented via DirichletBC on V.sub(i), V is the vector space (ie, V=W.sub(0) where W is the mixed T-H space) of velocity and i is the direction perpendicular to the boundary that you specify this ‘no-penetration’ B.C.

Or you can search symmetric boundary condition, and there are few examples.

3

Thank you! For your first suggestion, I guess it works for boundary of say rectangular domain, right? But for general domain, the out-normal may not align with the x or y direction.

4

See for instance the multipoint constraint extension to dolfinx: https://github.com/jorgensd/dolfinx_mpc/blob/master/python/demos/demo_stokes.py
You could Also consider using Lagrange multiplers with the Mixed dimensional functionality introduced in: https://arxiv.org/abs/1911.01166

2 Likes
5

Thank you very much!

6

Adding to @dokken’s list of methods: Nitsche’s method.

1 Like
7

Thank you very much!