Drafty draft - #1293

Co-authored-by: Erik Faulhaber <44124897+efaulhaber@users.noreply.github.com>

Co-authored-by: Erik Faulhaber <44124897+efaulhaber@users.noreply.github.com>

…rticles.jlOpen into more_semi_refactor

…L_geoms

# Conflicts:
#	docs/src/tutorial.md

# Conflicts:
#	README.md
#	docs/src/getting_started.md
#	docs/src/index.md
#	docs/src/overview.md

# Conflicts:
#	README.md
#	docs/src/getting_started.md
#	docs/src/index.md
#	docs/src/overview.md

…rk/TrixiParticles.jl into check_math_in_docs

…' into bug_fixed

# Conflicts:
#	NEWS.md
#	test/schemes/boundary/open_boundary/characteristic_variables.jl

The third vertex of the inlet and outlet faces in
`examples/fluid/poiseuille_flow_3d.jl` spanned a diagonal edge, which is
rejected by the new orthogonality check in `spanning_vectors`.
Use the fourth corner of the rectangular cross-section instead, so that
both spanning edges are axis-aligned and orthogonal.
This also fixes the failing example tests
`fluid/poiseuille_flow_3d.jl (WCSPH)` and `fluid/pulsative_channel_flow_3d.jl`.

- Pick up the example fix from #1202 (orthogonal inlet/outlet face
  vertices in `examples/fluid/poiseuille_flow_3d.jl`).
- Restore the orthogonal 3D face in the `integrated variables` testset,
  which was lost when merging #1203 (that rewrite of
  `characteristic_variables.jl` still used a non-orthogonal face that is
  rejected by the new orthogonality check in `spanning_vectors`).

# Conflicts:
#	NEWS.md
#	docs/src/systems/boundary.md
#	docs/src/systems/entropically_damped_sph.md
#	docs/src/systems/fluid.md
#	docs/src/systems/implicit_incompressible_sph.md
#	docs/src/systems/total_lagrangian_sph.md
#	docs/src/systems/weakly_compressible_sph.md
#	src/callbacks/mechanical_work_calculator.jl
#	src/callbacks/stepsize.jl
#	src/general/semidiscretization.jl
#	src/schemes/fluid/entropically_damped_sph/rhs.jl
#	src/schemes/fluid/surface_tension.jl
#	src/schemes/fluid/weakly_compressible_sph/rhs.jl
#	test/callbacks/stepsize.jl
#	test/general/custom_quantities.jl
#	test/schemes/fluid/calculate_dt.jl

# Conflicts:
#	src/general/corrections.jl

Fix conflicts in EDAC and WCSPH RHS:
- adopt mapreduce_neighbor / add_dv_* functional API from origin/main
- preserve gradient/force correction splitting from stack (gradient_correction for pressure/shifting, force_correction for free-surface)

…ecycle to restore stack diff

# Conflicts:
#	src/schemes/fluid/entropically_damped_sph/rhs.jl
#	src/schemes/fluid/weakly_compressible_sph/rhs.jl
#	test/general/corrections/lifecycle.jl