Fix non-conservative mortars for P4estMesh 3D

[amrueda]

A unique mortar flux used to be computed from the small interfaces and then projected to the big elements and copied to the small elements. This works for conservation laws. However, for non-conservative equations, the mortar flux should be computed from both sides of the mortar due to its asymmetric nature.

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.36%. Comparing base (4a81e00) to head (f19d4d8).
Report is 1 commits behind head on main.

Additional details and impacted files

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  Coverage   96.36%   96.36%           
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  Files         477      477           
  Lines       37753    37760    +7     
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+ Hits        36378    36385    +7     
  Misses       1375     1375           

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[ranocha]

https://github.com/trixi-framework/Trixi.jl/actions/runs/11460837729/job/31888478768?pr=2127#step:7:11430 looks like a real error

[andrewwinters5000]

https://github.com/trixi-framework/Trixi.jl/actions/runs/11460837729/job/31888478768?pr=2127#step:7:11430 looks like a real error

It seems like the parabolic solver is attempting to use the surface_flux from the hyperbolic solver instead of BR1. This would (possibly) explain why it is throwing an error that flux does not exist for the equations_parabolic. Although I am not certain.

[andrewwinters5000]

I think I tracked down the issue. On TreeMesh there is a specialized version of calc_mortar_flux! that dispatches on the AbstractParabolicEquations type (https://github.com/trixi-framework/Trixi.jl/blob/main/src/solvers/dgsem_tree/dg_3d_parabolic.jl#L722-L726). However, no such equivalent is implemented for the P4estMesh, so I believe the parabolic solver on P4estMesh is actually grabbing the hyperbolic variant (https://github.com/trixi-framework/Trixi.jl/blob/main/src/solvers/dgsem_p4est/dg_3d.jl#L517-L521). In turn, I think this causes the issue of attempting to call the "wrong" flux later.

[amrueda]

I think I tracked down the issue. On TreeMesh there is a specialized version of calc_mortar_flux! that dispatches on the AbstractParabolicEquations type (https://github.com/trixi-framework/Trixi.jl/blob/main/src/solvers/dgsem_tree/dg_3d_parabolic.jl#L722-L726). However, no such equivalent is implemented for the P4estMesh, so I believe the parabolic solver on P4estMesh is actually grabbing the hyperbolic variant (https://github.com/trixi-framework/Trixi.jl/blob/main/src/solvers/dgsem_p4est/dg_3d.jl#L517-L521). In turn, I think this causes the issue of attempting to call the "wrong" flux later.

Thanks for checking, Andrew. I wonder why this issue is only showing in this PR. I only changed the name of the variable fstar. 🤔
I’m trying to fix it.

[DanielDoehring]

I think I tracked down the issue. On TreeMesh there is a specialized version of calc_mortar_flux! that dispatches on the AbstractParabolicEquations type (https://github.com/trixi-framework/Trixi.jl/blob/main/src/solvers/dgsem_tree/dg_3d_parabolic.jl#L722-L726). However, no such equivalent is implemented for the P4estMesh, so I believe the parabolic solver on P4estMesh is actually grabbing the hyperbolic variant (https://github.com/trixi-framework/Trixi.jl/blob/main/src/solvers/dgsem_p4est/dg_3d.jl#L517-L521). In turn, I think this causes the issue of attempting to call the "wrong" flux later.

Good spot, I do not really recall why this was implemented in this way in

#1765

[amrueda]

Thank you all for your comments. The problem was that I didn't realize that calc_mortar_flux! and mortar_fluxes_to_elements! from the hyperbolic semi-discretization are used by the parabolic semi-discretization with specialized functions. After modifying the hyperbolic semi-discretization, I had to update the specialized functions. This is now done in f19d4d8. In my opinion, the PR is ready to be reviewed.

[andrewwinters5000]

LGTM, thanks for fixing the 3D version @amrueda ! It should be straightforward to port this to the other dimensions and mesh types.

[ranocha]

Thanks! Since @andrewwinters5000 has approved this PR, I will merge it. Who will fix the remaining dimensions and mesh types?