FacetNormal of internal boundary

Question

Hi all,

I encountered an problem when I tried to evaluate FacetNormal on the internal boundary, and hope someone could provide more insight to properly evaluate this. Basically, my domain has two parts connecting together, and I need to apply robin boundary condition on this interface.

Here is my previous post (my equation and boundary conditions). In short, my mistake on previous post is that I did not account for the normal vector orientation. Because I would like to work on more generalized geometry, here is my fix to previous problem by defining normal vector, and do a dot product.

n = FacetNormal(flowing_layer_mesh)
...
F = ... + dot(n, local_shear_rate*Epsilon*Lambda*u*(1.0-u))*v*dsTop + dot(n, local_shear_rate*Epsilon*Lambda*u*(1.0-u))*v*dsBottom

This approach appears to work pretty well if I try to evaluate the curve boundary on the outside of my mesh. However, this method appears to fail when I try to evaluate boundary line that is inside my mesh (which in this case, it is a curve interface between two regions). The reason I suspect it is this part fails is that I basically see exactly the same behavior as in my previous post.

Any help would be appreciated! Thanks!

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Answer 1

Hi dengzhekai,

Indeed the above paragraph is fairly minimal, so I am not entirely sure this will help.
But one thing you have to change in order to work with internal boundaries is your measure (dS instead of ds).

dSinterface = Measure("dS", subdomain_id=1, subdomain_data=boundary_parts)

Comments

Hi meron, I think this might be helpful and I was using "ds" to measure the ds_interface. I change it to "dS", but the program does not run, with error message

Unable to perform just-in-time compilation of form.

Any ideas ? Also, I have edited so that It now has the full code and related gmsh code.

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Hi!

Indeed when you run your code you encounter the error "Discontinuous type Argument must be restricted." You have to restrict when integrating over interior facets (*dS) to the positive or negative side of the facet or average (using ('-'), ('+') or avg(), you can check ufl-user-manual or look here

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Thanks for the reference. I think this resolves my issue. Thank you.