How to mirror a mesh and a solution vector to remove quarter symmetry for post-processing?

Question

Dear all,

I have a problem of a wave traveling through a quarter section of a cylinder. I need to enforce symmetry with y and z planes. So far, this is no problem.

In the next step, I need to do some computations with the surface normals (on facets and points) and integrate patches over surface nodes. If I integrate on my quarter-domain, facets that touch the boundaries are not integrated correctly because they do not see the normals from the other side of the symmetry planes and have only 1/2 the area. If I use periodic boundary conditions, the normals are not "mirrored" correctly, but made periodic...

Is there an easy way to just mirror a mesh and a solution vector on two planes to remove the quarter symmetry for post-processing my calculations?

Alternatively: I am interpolating the facet normals into a CG 1 function space on the surface to get point normals. Is there a way to make this procedure aware of the symmetry planes?

Answer 1

Hi,

I believe I do something somewhat similar, though my problem is not as complex. I have a function u(x,y) defined on a quarter-pipe domain. To manipulate the function u on the full pipe, I construct a function g(x,y) = u(abs(x),abs(y)) on the full domain. If this sounds like something that would be useful to you, I can provide some sample code.