Accessing the Normals for Gmsh

[Zack-With-A-K]

Hi! I am using Firedrake to model blood flow in the aorta. We have a solution for the velocity and pressure; however, what we really want is to calculate the normal stress acting on the wall of the aorta. To do this, we obviously need the unit normal vector at each face on the outside of the mesh. When we tried using FacetNormal, it didn't seem get exactly what we needed to perform the computation. We've also played around with using Paraview's filters (especially programmable) to help do this, but were still struggling to get exactly what we needed. Likewise, biggest issue there is accessing only the surface of the mesh and calculating the normal. So if you have any ideas for how to do this in either Firedrake or Paraview (or a mix), we would really appreciate it!

[sghelichkhani]

I might be misunderstanding what you mean by "it did not seem what you needed": but a similar problem for us is calculating normal stresses on a specific boundary in gadopt (stokes for mantle convection). There I used FacetNormal in a surface integral. Might that be what you need?

https://github.com/g-adopt/g-adopt/blob/1bd977805fe4949f3db866c706e3756cb20b4cb6/gadopt/stokes_integrators.py#L818
with n being FacetNormal(mesh).

[Zack-With-A-K]

Thank you so much for your response! What equation exactly you were solving with that setup? I tried doing something similar for our situation with

W = FunctionSpace(mesh, "CG", 1)
phi = TestFunction(W)
sig = Function(W)
 vu = TrialFunction(W)
a = inner(phi,vu) * dx 
L = - phi * dot(dot(grad_u_func, n), n) * dx # (here grad_u_func = grad_u_func.interpolate(grad(u))) where u is solved velccity
solve(a == L, sig, bcs=bcs, solver_parameters={"fieldsplit_0_pc_factor_mat_solver_type": "mumps"})

but ran into an error: raise RuntimeError("%r defined on incompatible FunctionSpace!" % r). So I was also wondering if you had encountered any difficulties with that?

[sghelichkhani]

This does not seem to be relevant to anything other than your bcs. My hunch is that your bcs are not compatible with W

[dham]

Yes. this example is incomplete. Please supply a Minimal Failing Example (i.e. a short piece of code that actually runs and exhibits the error).