[Gfs-users] Gerris multiple questions

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Xavier Barthelemy

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Jan 22, 2020, 12:25:40 AM1/22/20
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Hi Guys, 


I am reviving the Gerris mailing list for a few technical questions.
I know most of everyone has transitioned to Basilisk, which our team will do eventually. 
We are polishing a work we started a while ago using gerris, that's why we have to use it. 


We are working on wave breaking, and trying to reproduce not only the results of a monophasic solver, but also from other 2 fluids VOF-based solver.


We reached a point where everything works globally, but as it is said, the devil is in the details. We would love to have the community's recommendations.


Gerris wave flume is configured using the reduced gravity hypothesis.

the colour function interface is smoothed in T1, as advised on the tutorials.

the flume is of finite length, with a wave maker on one end, and a higher viscosity buffer zone on the other end.


The wavemaker is build by imposing (U, V, W, P) on the boundary, and mass conservation is giving the T(y,t) BC

The transition from the "normal" domain to the buffer zone is continuous and derivable.


top boundary condition is non viscous.

interface is symmetrically refined  in air and water up to level 9, 10, 11, depending the case.


  • First a convergence question:

We have played with the Poisson solver, changing the max iteration number and also the residue value:

Stephane1.PNG
Even when relaxing the number of iterations, it seems there still is a convergence problem. The two cases show evidently two different results.
Fortunately, it doesn't modify significantly the below-the-crest speeds:
Stephane2.PNG
  • When we look at the output BC, 2 solutions (so far) appears:
1-non-slip, with the below results,  
2-or Neumann BC, outflow type in gerris

When the air pressure in the middle of the tank is plotted:

Stephane3.PNG 
or, with a better scale:

Stephane4.PNG

so, adding an outflow BC destabilise the solver, something which is known.
What would be the right way to do it in this case, to let the solver converge?

  • Then another question on the interfacial speeds:
the interface is defined at T=0.5
We then check the kinematic BC on the interface is valid.

Stephane5.PNG
Stephane6.PNG



Our analysis depends on the local energy flux, which requires the precise computation of velocity at the crest and just below the crest.
the problem is then the existence of a interface boundary layer. so the question is what is the correct speed at the interface?

Because of the smoothing to stabilise the simulation, the speed maximum is 2 cells below the T=0.5 line, and which gives some false positive in our breaking criterion.
We would like to solve this:
"The crest tracking issues seem to have been resolved in these runs, with both the low-pass and wavelet smoothing giving good results. The next step is determining the correct way to calculate Fx/E. Recall that we have seen a below-interface jet in all runs that have been completed - regardless of boundary condition, resolution, surface tension or viscosity. This creates an Fx/E maxima 2-3 grid cells below the interface - which is not in agreement with the JFM boundary element model results. " says my PhD student
so we got inspired by: 
Stephane7.PNG

to rebuild the velocity using density ratios:
"Recall that the attached paper adjusted the velocity at the VOF interface by the ratio of the cell density to the water density. I tried this previously and it did not look sensible – but I have now realised that I should have used the smoothed VOF tracer (T1, with which density is assigned in the model) instead of the unsmoothed tracer T.

 

The result is shown in the attached image (purple dashed line). The effect is to slightly reduce the magnitude of the jet.

 

Also shown is a different formulation (purple dot-dash), where the velocity is calculated by:

 

U = U + U*((1-T1)/T1)

 

This gives a very nice looking extension to the exponential profile (although the maxima overshoots the T=0.5 contour by 1 cell).

 

There is an option to try use this modified velocity in the wave tracking. While the larger velocity seen here will increase Bx, this will be offset by applying rho as a function of T1 (which reduces rho in the interface layer."


here are the plots:
Stephane8.PNG

We have reached my limits on ideas on the question, and we need enlightenment from the community to answer this very important question (for us).

  • also how can we solve exactly the interfacial stresses to compute the energy exchanges?

Thanks for reading us to the end, and I would appreciate if you can help us.
Thanks in advance for your time and ideas
Cheers
Xavier



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