How to transform the solution on fixed (reference) mesh to that on current (physical) mesh?

[Lex Lee]

Hello,

In recent several months, I have been studying Prof. Thomas Wick's ALE transformation method and his implementation codes structure for the FSI problem. (https://media.archnumsoft.org/10305/). In his online codes file (from line 2695 to 2710, https://media.archnumsoft.org/10305/doc/step-fsi_8cc_source.html), he stated that 

"However, we emphasize that the FSI problem is computed on a fixed mesh (instead of moving the mesh as done in other references; we refer the reader to the accompanying article and the comments made therein). For this reason, the output of the solution in *.vtk format corresponds to the solution on the fixed mesh and, therefore, in a visualization program, the reader has to post-process the solution. We also refer to the MappingQEulerian in the deal.II library, which is able to transform the solution to the current (i.e., the physical mesh) "

The attached .vtk file is one of the graphical outputs. As you can see, the elastic beam doesn't vibrate as the solution is computed and outputted on a fixed mesh, not on the current mesh. (source codes for version 9.0 of deal.ii, http://www.thomaswick.org/gallery_engl.html)

Does anyone know the details (or give me a hint) that how to process the solution in .vtk format, namely, transforming the solution on a fixed mesh to that on a physical mesh?

I appreciate any comments from you guys. 

Best,

Lex

[Thomas Wick]

Hi Lex,

the difficulty is that the FSI problem is solved in the fixed reference domain \hat\Omega.
To have the solution in the physical domain \Omega(t) you need to apply the ALE transformation:

A(x) = x + u,

where x are the coordinates of the mesh and u the displacements.


You have three options:

A) In the visualization software visit you need:
1. OpAtts
2. Transform
3. Displace
--> Define therein the displacement operator (vector-valued)
    with the help of x_dis and y_dis.

Activate the operator and apply it to the solution you want to display.


B) In paraview, a similar operator exists that I however do not know in detail.


C) You could take the solution vector in the code and apply directly
    therein the displacements u  to the coordinates x
    and then output the solution.

Best regards,

Thomas W.

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

Welfengarten 1
30167 Hannover, Germany

Tel.:   +49 511 762 3360
Email:  thoma...@ifam.uni-hannover.de
www:    http://www.ifam.uni-hannover.de/wick
www:    http://www.thomaswick.org
++++--------------------------------------------++++
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-- 

Am 22.11.19 um 09:12 schrieb Lex Lee:

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