Remove normal_direction_ll for nonconservative terms

[patrickersing]

This PR simplifies the nonconservative terms to only depend on a single averaged normal_direction, instead of both normal_direction_average and normal_direction_ll (see #2049).
This should also enable setting boundary conditions for nonconservative terms #1445

[github-actions]

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[patrickersing]

As expected changing the normal directions caused slightly different results and with that some failing mhd tests.
The p4est and t8code test results are almost the same and only the psi value fails testing with differences in L2 between 1e-8 and 1e-10.
For UnstructuredMesh and StructuredMesh there are more failing tests, but the differences in the L2-Error remain relatively small between 1e-5 and 1e-8. The reason is probably that we use a very coarse mesh for the testing, with only four elements per dimension, which leads to larger differences in the normal direction.
Entropy is still conserved in all relevant tests.

For validation I additionally ran convergence tests using structured_2d/elixir_mhd_alfen_wave.jl and compared the result with the previous implementation using normal_direction_ll. The results show almost identical convergence rates.

polydeg=3, normal_direction_average:

polydeg=3, normal_direction_ll:

polydeg=4, normal_direction_average:

polydeg=4, normal_direction_ll:

Looking at these results, I think it would be fine to introduce the averaged normal direction and update the test values.
It would be great if someone working with MHD (maybe @amrueda @SimonCan @andrewwinters5000) can have a look at this and let me know if they think this is fine or if more validation is needed.

Another open problem is that the test dgmulti_2d/elixir_mhd_reflective_wall.jl is failing. @jlchan do you have any idea why this test could be failing?

[jlchan]

Another open problem is that the test dgmulti_2d/elixir_mhd_reflective_wall.jl is failing. @jlchan do you have any idea why this test could be failing?

Thanks for testing it out in DGMulti too! I'll take a look this afternoon.

Since the test is failing due to domain error (negative density or pressure) I think it's a real failure. My guess is that it's related to the boundary condition imposition

Trixi.jl/src/solvers/dgmulti/dg.jl

Lines 555 to 560 in aaf0166

	noncons_flux_at_face_node = boundary_condition(u_face_values[i, f],
	face_normal,
	face_coordinates,
	t,
	nonconservative_flux,
	equations)

since all the other MHD tests still pass.

[patrickersing]

Since the test is failing due to domain error (negative density or pressure) I think it's a real failure. My guess is that it's related to the boundary condition imposition

That makes sense. I just looked at the boundary conditions that are used in the elixir and noticed that BoundaryConditionDoNothing needs to be adapted. Currently this always calls the flux function (even if we call it with the nonconservative term) so this definitely imposes a wrong boundary condition.

I will try to replace this with

@inline function (::BoundaryConditionDoNothing)(u_inner,
                                                outward_direction::AbstractVector,
                                                x, t, surface_flux, equations)
    #return flux(u_inner, outward_direction, equations)
    return surface_flux(u_inner, u_inner, outward_direction, equations)
end```

[jlchan]

@patrickersing looks like your new BoundaryConditionDoNothing fixed the issue; the failing tests for unstructured_dgmulti now just seem to be due to floating point differences.

[DanielDoehring]

Once this is ready to go we can schedule the next breaking release 0.9, cf. #1997

[andrewwinters5000]

LGTM! I just left one question for Andrés. It would be good to get this PR ship-shape and ready for the next breaking release. Can you have a look @amrueda or @SimonCan as you both more actively work with the MHD system.

[andrewwinters5000]

This would also be true in 3D but the subcell limiting implementation is not done (yet) right @amrueda ? That is why a corresponding comment in the 3D ideal GLM-MHD file is not done?