Dear all!
I would like to learn Openfoam, and if I get over the first tutorials, I want to solve FSI problems to study the flight behaviour of kites and paragliders.

I'm not sure whether my mathematical background is sufficient to finish this project. For this reason I need some explanation what is meant by weak or strong coupling in fluid structure interaction.

Is the strength of a coupling a physical property of the modeled scenario, or is it a characterization of the numerical method?

To give an example, if two masses are coupled by a stiff spring, is this coupling considered strong compared to the same masses coupled by a soft spring?

From the presentation powerlab.fsb.hr/ped/kturbo/OpenFOAM/slides/MIT2007FSI_14Jun2007.pdf I get the impression that the difference between weak and strong coupling lies in the discretization and not in the physical system. What is then the exact definition of the strength of a discretization? Is a coupling weak, if all eigenvalues of the discretized matrix are smaller than 1?

And finally, how can I decide when weak or strong coupling is necessary?

Lots of questions ... can you answer one or two of them?

Thank you
Hajo

[dmoroian]

Hello Hajo,
First I'm not an FSI expert, but I will share my knowledge.
Coupling strength of a fluid structure interaction has correspondence in both physical and numerical space.
In physical space it means for instance how large is the influence of the solid deformation (caused by the flow) on the fluid. If you study the stress induced by a stream flowing over a steel cube, then the deformation may be considered small and consequently the coupling weak. This has an immediate correspondence in the numerical space: solving such a problem requires only to transfer the pressure from the fluid towards the solid at the interface.
If you study a paraglider, then it is likely that a small variation in pressure field will induce large deformations in the solid. When a large solid deformation occurs, then also the flow is influenced. This is an example of a strong coupling between the flow and solid fields. Of course this has a direct link to numerics. It is no longer enough to transfer the pressure from the fluid to the solid. Now it is necessary to bring back the information about the geometrical change too.
This is a simple view. Especially in the numerical part there are flavors of how strong coupling you can use (explicit or implicit).

I hope this is helpful,
Dragos

Hello Dragos,
thank you for the explanations. I'm not sure, if I got you right, because as you say the physical coupling must correspond to the numerical scheme. I'd consider the steel cube much stronger coupled than a soft body like a paraglider, because a small deformation of the steel results in large stress.
I suppose you mean that you can describe the steel cube as undeformable, so that it is basically a fixed boundary, but this is no longer an FSI problem.

Irrespective of this last point, I'd like to know whether my impression is correct, that a numerically strong coupling ("NSC") is a sort of general purpose coupling, because it would also work on physically weakly coupled ("PWC") systems? And a NSC wouldn't be too inefficient for PWCs, because a rapid relaxation could be used so that convergence is established after very few iterations?

Can you recommend a textbook which covers this question on coupling strengths in FSI problems in more than one or two sentences, or maybe a paper or a thesis especially on this topic?

Thanks
Hajo

[dmoroian]

Hello Hajo,

Two important members of this forum have published a paper on this topic: FSI

I regard the strong coupling between two domains as the influence that each exerts on the other.
In the steel cube example, only the fluid puts some pressure on the solid, whereas the solid does not influence the fluid. This is sometimes called one way coupling (which is a weak coupling).
On the other hand a paraglider will modify its shape under the influence of the flow pressure, and by doing that will act on the flow changing the velocity distribution. This is sometimes called two way coupling (which is a strong coupling).

I hope this is helpful,
Dragos

Dear Dragos,
I begin to feel stupid, because I cannot follow what you are saying. Your last differentiation between weak and strong coupling is the exact opposite of my understanding. But if that is consensus, I'll adapt the terminology.

Next point is the "FSI" link you posted. This paper mentions the FSI problem a few times but shares absolutely no details about the method. Instead the vibrations of an isolated cantilever beam and a wing are studied. Apparently the paper is to be continued in a second publication. Is that one already available?

Hajo

[dmoroian]

Hi Hajo,
As I said previously, my experience in FSI is very limited, and I might be wrong in what I say.
You don't have to feel stupid just because you don't have the same view over the problem as I do. But if you want to continue on this topic you have to come to a common language with the others.
The paper that you saw contains a description of an FSI problem (indeed only the structural solver is presented). If you fill its content is not enough, then I suggest you contact the authors or follow the broad reference list (ref. 14 is one example).

Dragos