# Finite elements algorith for a fluid in a tube with an elastic obstacle (Fluid-Solid coupling)

I want to solve the model of a tube with an elastic obstacle, something like a simple model of an vessel with a valve. The fluid is given by an evolutionary incompressible Navier--Stokes equations, and the obstacle for elasticity equation.

In the step 46 of dealii appears a simple way to manage this kind of problems

If I understand correctly, the algorithm proposed is the following:

1. Solve the fluid problem assuming that on the elastic obstacle the velocity is equal to zero.
2. Use the velocity fluid solution on the boundary of the solid as a boundary condition in the elasticity problem, and then solve the elastic problem.
3. Update the fluid-solid mesh.

I'm understanding correctly? In that page says that is only an academic algorithm, with the goal of explaining the implementation, and is not a realistic FSI model.

I have two questions:

1. This algorithm looks easy to program because it uses existing solvers. Do you know if it is an algorithm used for FSI? (a one-way algorithm perhaps).

and my main question:

2. Which is the Finite Elements algorithm for this kind of coupled problems? I searched a lot on internet, because surely someone already proposed an algorithm, but I could not find an algorithm.

• I think you should ask questions specific to deal.II on the deal.II forum :-) Sep 28, 2020 at 12:51
• Thanks @WolfgangBangerth, do you say in the deal.II e-mail list? Or exists a forum? Sep 28, 2020 at 22:52
• The mailing lists (which also has a forum-like interface: groups.google.com/g/dealii ). Sep 28, 2020 at 23:49
• So the solid is not rigid? Sep 29, 2020 at 23:09
• @MaximUmansky the obstacle is not rigid. The boundary of the tube is rigid (for the moment) Sep 30, 2020 at 3:47