Implement coupling between meshes in one simulation

[efaulhaber]

We implemented a new SemidiscretizationCoupled which bundles multiple semidiscretizations and runs them in parallel with synchronized time steps. These semidiscretizations can be coupled using the new BoundaryConditionCoupled. When this boundary condition is used, values at a specified boundary of another mesh can be used as boundary condition.

We adapted the visualization code to plot coupled semidiscretizations as well: This is the advection basic example, but we split the mesh in two parts to use two semidiscretizations and a coupled boundary in between.

New examples are the coupled basic example above and the Euler source terms example on a ring (in 2D) and a cubed sphere (in 3D). These two are shown below using the visualization in https://github.com/trixi-framework/Trixi2Vtk.jl/pull/31.

Restart support has not been implemented in this PR.

[codecov[bot]]

Codecov Report

Merging #553 (f8b8a6c) into main (dc30dba) will increase coverage by 3.70%. The diff coverage is 91.90%.

:exclamation: Current head f8b8a6c differs from pull request most recent head a126baf. Consider uploading reports for the commit a126baf to get more accurate results

@@            Coverage Diff             @@
##             main     #553      +/-   ##
==========================================
+ Coverage   89.15%   92.86%   +3.70%     
==========================================
  Files         226      224       -2     
  Lines       18816    18785      -31     
==========================================
+ Hits        16775    17443     +668     
+ Misses       2041     1342     -699     

Flag	Coverage Δ
unittests	92.86% <91.90%> (+3.70%)	:arrow_up:

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/Trixi.jl	66.67% <ø> (ø)
src/callbacks_step/analysis_dgmulti.jl	98.63% <ø> (+49.30%)	:arrow_up:
src/meshes/tree_mesh.jl	83.78% <0.00%> (-1.15%)	:arrow_down:
...discretization/semidiscretization_euler_gravity.jl	88.44% <50.00%> (-2.93%)	:arrow_down:
src/solvers/dgsem_p4est/dg_2d.jl	98.55% <50.00%> (-0.47%)	:arrow_down:
src/solvers/dgsem_p4est/dg_3d.jl	98.64% <50.00%> (-0.33%)	:arrow_down:
src/semidiscretization/semidiscretization.jl	90.54% <66.67%> (-1.01%)	:arrow_down:
src/meshes/mesh_io.jl	95.05% <76.00%> (+0.78%)	:arrow_up:
src/solvers/dgsem_structured/dg.jl	86.67% <88.46%> (+2.46%)	:arrow_up:
src/callbacks_step/stepsize.jl	96.00% <90.00%> (-1.67%)	:arrow_down:
... and 67 more

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[efaulhaber]

We don't understand why the documentation job is failing.

[sloede]

We don't understand why the documentation job is failing.

See for the immediate cause https://github.com/trixi-framework/Trixi.jl/pull/553/checks?check_run_id=2544365213#step:5:11

[efaulhaber]

For some reason, the L2 errors rho_v1 and rho_v2 are flipped on macOS for one test case.

[efaulhaber]

Why the hell are rho_v1 and rho_v2 errors interchanged in CI compared to my system for the elixir_euler_cubed_sphere_coupled!?