Lid-driven cavity with flexible bottom

Hello precice-developers and -community,

after testing my DUNE-adapter with the flexible flap tutorial in 2D/3D, some further programming
and validation, I wanted to give the “lid-driven cavity with flexible bottom” scenario a try.

The scenerio looks like that, but is in 3D:

The velocity of the to wall is given as: vbar = 1-cos(2pit/5)

I found an openFoam configuration of that case in the mbdyn-adapter section that looks quite
good (despite the fact that the last update was done over a year ago). I created the mesh for the bottom wall, that represents the membrane, with linear 8-node hexa elements and one element over the thickness. The nodes of fluid and solid mesh coincide. The first 5s of the simulation run fine and look similar to the expected results. My problem is that the deformation of the membrane is just increasing and no oscillating behavior is occurring.

The picture shows the overall membrane displacement in y-direction (left) and additionally the y-displacement of the membrane-midpoint over the simulation time (right):

After 10s the simulation crashes, due to the huge deformation of the mesh. Additionally, the effect of the time-dependent velocity of the lid can be slightly seen at 5s.

Maybe someone has experience with that case and can give me some tips how to model the membrane/bottom wall properly or might has some ideas what could be the problem.

Just for completeness the precice-config:
precice-config.xml (3.2 KB)

Max

Hi Max,

I also simulated the 3D case in my dissertation, Section 3.7.3.
I did use “real” 2D membrane elements though.
Maybe the values there help?
Does your simulation work if you simply make your structure very stiff?

Benjamin

Hey Benjamin,

I tried to run the case with the values of your dissertation. The deformation is still increasing till
it crashes due to the huge mesh deformation.

Afterwards I tried your suggestion of using a stiffer structure, which resulted in a better outcome.
Graphs show again the vertical displacement of the membrane midpoint.

First with the parameters of the elastic flap case:
E = 400000
v = 0.0
rho = 3000

And in a second run with:
E = 2100000
v = 0.0
rho = 8000

The periodical change of the velocity and thus the oscillation of the structure (T=5s) can be seen quite clearly in both cases I would say. The scaling of the axis is nearly the same in both cases so for a stiffer structure there is less response, which also makes sense.

On the structure side I solve for linear elasticity, which normally allows only small deformations.
Could this maybe the reason for the nonphysical behavior for a very “flexible” material that allows large deformations ?

So, in principle you get the right behavior. There cannot be a huge problem

Yes, this can very well have an influence in that direction.
The other difference is that you use 3D elements. I guess that if make them thicker you will also get a smaller displacement.

So with E=25000, v=0 and rho = 500 the simulation is still going into the right direction. Reducing the Young’s modulus results in deformations that are too large.

I’m pretty sure it has something to do, that I always reference my stiffness matrix to the undeformed state. For large deformations this introduces an error that might be so large, that the deformation get’s way to big.

I’m actually quite happy with the results obtained with the parameters stated above, so I mark this as solution. Implementing a solver that can handle geometric nonlinearities (e.g. large deformations) might be a bit out of scope for me, at least right now.

Thanks for the help!

what is unit of E and rho?