Lagrange multipliers

[neverwoke]

Hello all. I am very new to the community but very eager to learn. I am wonder if there is an out-of-the-box support for using Lagrange multipliers on a boundary, to enforce rigid body motion in Stokes flow, similar to the work of Glowinski [1] or Hwang [2]?

[1] Glowinski, R., Pan, T. W., Hesla, T. I., Joseph, D. D., & Periaux, J. (2001). A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. Journal of Computational Physics, 169(2), 363-426.

[2] Hwang, W. R., Hulsen, M. A., & Meijer, H. E. (2004). Direct simulation of particle suspensions in sliding bi-periodic frames. Journal of Computational Physics, 194(2), 742-772.

[Wolfgang Bangerth]

On 08/08/2017 11:16 AM, neverwoke wrote:
> Hello all. I am very new to the community but very eager to learn. I am wonder
> if there is an out-of-the-box support for using Lagrange multipliers on a
> boundary, to enforce rigid body motion in Stokes flow, similar to the work of
> Glowinski [1] or Hwang [2]?

I'm not aware of a program that is available publicly that would do this
already, but such methods have definitely been implemented. You could, for
example, take a look at some of the papers by Angelo Frisani on this.

So the question is what you mean by "out of the box". It's possible, but it'll
require work like any other advanced numerical method.

Best
W.


--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Eldar Khattatov]

One way of using Lagrange multipliers on the boundary is to have an additional full dimensional space for them. With this you will be able to compute the boundary terms, but you will need to restrict the interior DOFs of this space by adding something like: 

(epsilon * lambda, mu)_Omega,   (where epsilon some very small number not to affect your theoretical accuracy)

to your system (so it becomes nonsingular). This is not the most efficient way of doing it, but it is very easy as Deal.II has everything you need for this approach out of the box.

Best,

Eldar