Fluid-Structure interaction

[Ramiro James Rebolledo Cormack]

Hi everyone.

I'm looking for a solver to solve a fluid-structure problem, like a heart valve: the valve is an elastic material, and the blood could be considered as an incompressible fluid (evolutionary incompressible Navier--Stokes equations).

In step-46 I see a Fluid-Structure interaction implemented in dealii

    https://www.dealii.org/current/doxygen/deal.II/step_46.html

but I'm not sure if it is appropiate to a more realistic problem.

I know that the first thing is to know what is the numerical method that we want implement, but I'm not sure what is the appropiated numerical method to solve this strong coupled problem.

My goal is to implement a model of a valve oppening and close due blood pressure (a cilindrical tube with an elastic obstacle in the middle). Do you think dealii could be an appropiate code to model this? Or is a too big problem?

The other possibility is to use commercial software (COMSOL or ANSIS), but due we don't know what they do to solve the problem, I could prefer to program "my own" solver, for example with dealii.

I suppose there must be many papers proposing algorithms for these types of coupled problems, but I have not found anyone explaining the mathematical aspects behind it. So I am very confused about how to implement this coupled problem.

I don't know if is too much to ask here,  if so, I apologize in advance.

In concrete, my questions are the following:

- what is the numerical algorithm to solve this coupled problem.

- and, is it possible to solve this with dealii? Or is a too big problem.

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Ramiro

[Thomas WICK]

Hi Ramiro,

step-46 can be indeed extended to "realistic" FSI (a student of mine did it some time ago; but requires a bit of work of course).
As alternative, my deal.II-like tutorial step can also serve the purpose

https://media.archnumsoft.org/10305/

with the code documented as a true deal.II tutorial step. The official version is based on 7.0.0.
You may find updates on my webpage

http://www.thomaswick.org/gallery_engl.html

in case of interest.

Other than this I guess Luca Heltai has also some codes online.

Best regards,

Thomas W.

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Thomas Wick
Leibniz University Hannover
www.thomaswick.org

Am 07.10.20 um 16:28 schrieb Ramiro James Rebolledo Cormack:

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Prof. Dr. Thomas Wick
Leibniz Universität Hannover (LUH)
Institut für Angewandte Mathematik (IfAM)
Arbeitsgruppe Wissenschaftliches Rechnen (GWR)

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[Jean-Paul Pelteret]

Hi Ramiro,

I would also suggest taking a look at the publication list to understand a bit better what can be achieved using deal.II (and, hopefully, how to do it). Here, for example, is some work done in vascular biomechanics, and the publication list has several other references to FSI.

@phdthesis{2017_31,
  author    = {A. M. De Villiers},
  title     = {A patient-specific FSI model for vascular access in haemodialysis},
  school    = {University of Cape Town},
  year      = {2017},
  url       = {http://hdl.handle.net/11427/24441}
}

Although I’m absolutely not an expert on the topic, I agree with Thomas that Luca’s work on immersed methods might be of interest to you when it comes to modelling the interaction between a highly deformable structure, such as a valve, and the fluid that surrounds it.

Best,

Jean-Paul

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[blais...@gmail.com]

Dear Ramiro,

You could also take a look at step-70 by Luca and I. It deplays a very prototype-ish fluid-structure interaction framework using immersed boundaries. I am sure Luca has progressed a lot on this issue since then. You can also look at software derived from Deal.II. Our group develops a full Navier-Stokes solver (https://github.com/lethe-cfd/lethe) based on deal.II. Extending it to a fluid-structure software could be done relatively simply if you want to use a non-monolithic coupling.

Best

Bruno

[Ramiro James Rebolledo Cormack]

Thanks Bruno, Jean-Paul, and Thomas.

I going to study each answer that you suggest me in detail, looks like it is exactly what I need.

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Ramiro