# curved boundaries

hi,
I’m an absolute beginner in lbm, and any patience shown towards my almost definitely trivial question would be really appreciated.
Is it possible to impose a velocity boundary condition for CURVED boundaries in 3D?Say, if you wanted to simulate 3D cylindrical pipe flow, with the no slip BC.
HELP NEEDED!!!
(I’ve looked at the research papers mentioned on lbmethod.org, but they only refer to straight walled boundaries…)

shubh

Hello,

have a look at this article. There are also other works related to that problem.

Timm

If you’re an absolute beginner I’d recommend starting with simulating 2d flow with velocity boundary conditions first. Having gained sufficient understanding from working with this you should be able to extend the boundary conditions to 3d, even curved boundaries.

Usually exploring the third dimension is quite trivial, allthough computationally intensive, once there is full understanding of the two dimensional case.

hey
thanks a lot for the suggestions
@timm
the research paper you refer to isn’t available at my institute, you mentioned other works, would you be so kind as to post a few names?

@ponja
even an article detailing velocity impositions for 2d flow would be greatly helpful…( for curved boundaries the von neumann approach as far as i can tell isn’t implementable, Ref [1])

[1]
Straight velocity boundaries in the lattice Boltzmann method
Jonas Lat and Bastien Chopard
University of Geneva,
Geneva, Switzerland
Orestis Malaspinas, Michel Deville, and Andreas Michler‡
Ecole Polytechnique F´ed´erale de Lausanne,
Lausanne, Switzerland
(Dated: April 8, 2008)

I have to have a look at my literature in the institute, but I will not return before Friday.
Tell you more then.

This one seems quite conclusive and should be available if you’re at any university.

http://portal.acm.org/citation.cfm?id=1365351

Note I just googled “lattice boltzmann curved boundaries”

With regards to von neumann not being implementable, I guess it would be if you were using a staircase but I suppose you’re after something more accurate which the article should provide.

## ponja Wrote:

I guess it would be if you were
using a staircase but I suppose you’re after
something more accurate which the article should
provide.

er… posters please note the beginner part , i’m more than happy with the staircase approach (for now)
could you (or anyone else of course) please elaborate upon how i would apply von neumann to a staircase boundary, or maybe refer me to a paper if you think it can be done…?

thanks again

shubh

btw, @timm
got the research paper you mentioned, heavy reading but working on it…

Ok this is straight of the top of my head so someone please correct me if I’m wrong.

I have no idea what kind of results you are going to get but it will be very interesting to see if you do implement this.

Basically you’re required to have relatively fine mesh spacing in order for the staircase to actually amount to something relatively similar to a curve. In any case look at at part of a curve. This would for example be the northeastern part of a circle.

``````
___
|__
|_
|_
|

``````

Yeah man that’s totally a curve. You know how the von neumann bc is applied yeah? Just assume that every _ is wall to the north and | is a wall to the east.

Have a look at those articles:
Gallivan, Noble, Georgiadis, Buckius. an evaluation of the bounce-back boundary condition for lattice Boltzmann simulations. Int J Num Meth Fluids 25 (1997) 249-263
Filippova, Hänel. grid refinement for lattice-BGK models. J Comput Phys 147 (1998) 219-228
Chang, Liu, Lin. boundary conditions for lattice Boltzmann simulations with complex geometry flows. Computers and Mathematics with Applications (2009)
Timm

thanks, looking…

I have used the approaches by Bouzidi et al. and Yu et al., They are quite stable and are 2nd order accurate. They are based on the bounce-back scheme but employ interpolations at the real wall position. The implementation is very simple, especially the one from Yu et al.
Here the references:

“A unified boundary treatment in lattice Boltzmann method”
D. Yu, R. Mei, W. Shyy
41st Aerospace Sciences Meeting and exhibit, AIAA 2003-953

“Momentum transfer of a lattice-Boltzmann fluid with boundaries”
M. Bouzidi, M. Firdaouss. P Lallemann
Phys.Fluids 13 (2002) 3452-3459