Mesh from Cahn-Hillard?

mesh
1

Hello,

I am currently working through the Cahn-Hillard-example and my interested peaked!
As I understand it, the equations models phase separation, so it can be used to procedural generate configurations with two phases.
So would like to now if we could:

  1. take the solution at a certain time step,
  2. declare i.e. a solid and liquid phase based on the solution function (something like )
  3. solve a fluid-flow on the whole domain?

For the record I am not so much interested in a complete solution, because I like to challenge my self, but rather interested how the software specific concepts of FENICS could be used to do this. If nobody dislikes this idea I would also like to use this post to link informations, code and resources to this challenge, and hopefully at one point post the complete solution.

2

The first partial solution for this problem seems to be found in this useful post:
Identifying subdomains from level set function on fenicsx
From what I understand we can use a “conditional” to identfy the subdomains.
The other suggestion of meshing the boundary seems not possible, since we do not know the the analytic solution.
To reduce the error we can do 2 things:

  • increase the number of elements
  • (recommended in the post) increase order of elements
    Therefor we have to rewite the tutorial to account for higher order elements load a certain example and use the conditional to identify the subdomains