Constrained Transport with AMR

[smressle]

Will constrained transport still result in the divergence of B being zero to machine precision when meshblocks are being created/destroyed during the simulation?

In my test problem (torus in Cartesian GR) it seems like the answer is no.

[c-white]

This could be a result of the GRUser coordinates numerically approximating areas and volumes. I will take a closer look at this.

[smressle]

I believe you may be right. The issue is not necessarily just that the areas are approximate, it's that they are not consistently approximate. That is, when you break down a cell face into four new smaller faces, the sum of areas will not necessarily equal the original area since the approximate area sqrt(-g) dx1 dx2 is evaluated at the face center. Then the magnetic flux will change because of this.

That's my guess. So it is only a problem with GRUser coordinates and AMR when split faces into smaller ones. I don't see an obvious solution, but I also suspect the errors introduced are small and probably not important since CT will keep the problem from multiplying. I also suspect that HAMR has the same problem because their coordinates are quite complicated and they compute areas in the same way, though I think the magnetic fields are cell centered there so I don't know if that changes anything.

[smressle]

I should say, in general there seems to be no obvious solution. For the specific case of cartesian KS coordinates you can just integrate everything exactly. Easier too because sqrt(-g) =1. You would think that because of this the numerical calculation of areas with sqrt(-g) would be nearly exact, but maybe not.

[c-white]

Yeah, the general solution is a bit tricky. As a test of the specific case here, if you overwrite Real Determinant(const AthenaArray<Real> &g) to just return -1, does AMR work better?

[smressle]

Trying now