Fix BXs consistency accross mpi decomposition

[glesur]

This PR fixes a long-standing issue causing the face-centered magnetic field component B (referred to as BXs) to drift at MPI subdomain boundaries during long integrations. The drift occurs because neighboring subdomains may compute slightly different edge EMFs—likely due to roundoff differences—resulting in inconsistent BXs values across shared boundaries.

This bug is subtle and can manifest in several ways:

• A sudden increase in div(B) after restarting from a dump file. Because the dump stores only one of the two possible BXs values at each subdomain boundary, any accumulated mismatch becomes visible upon restart.
• Unexpected or non-physical BXs values at subdomain edges when using vector potentials.

Historically, these edge zones were not exchanged, under the assumption that each subdomain’s computed values were sufficient. In practice, this allowed roundoff-level discrepancies to accumulate over time.

This PR introduces a consistent synchronization rule: the BXs value from the left side (=start) of each subdomain is treated as the authoritative value and overwrites the corresponding right-side value of the left-side neighbour. This ensures deterministic and stable edge values. The change increases the communication cost by roughly ~5% due to the larger exchange buffer.

Finally, note that a similar issue can also arise in serial runs with periodic boundary conditions, and this PR fixes that case as well.

Because of these changes, this PR represents a major refactoring of the MPI exchange routines and boundary conditions logic, that all now relies on pre-defined bounding boxes. The new edge zones are now handled only for internal and strictly periodic (i.e., non–shearing-box) boundary conditions, simplifying and unifying the overall approach.

[Copilot]

Pull request overview

This PR resolves a critical issue causing face-centered magnetic field components (BXs) to drift at MPI subdomain boundaries during long simulations. The fix implements a consistent synchronization strategy where the left-side subdomain's BXs value overwrites the right neighbor's value, ensuring deterministic edge values. The solution also handles periodic boundary conditions in serial runs.

Key Changes

• Major refactoring of MPI exchange routines with new Exchanger class and bounding box-based logic
• EMF exchange now overwrites rather than averages to eliminate accumulated roundoff errors
• Extended test coverage to include MPI and improved tolerance for numerical precision

Reviewed changes

Copilot reviewed 32 out of 33 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
src/mpi/*.{cpp,hpp}	Complete refactoring: moved MPI/Buffer classes to dedicated directory with new Exchanger class
src/fluid/constrainedTransport/EMFexchange.hpp	Changed EMF exchange from averaging to overwriting left-side values
src/fluid/constrainedTransport/enforceEMFBoundary.hpp	Enabled ENFORCE_EMF_CONSISTENCY and simplified periodic boundary logic
src/fluid/boundary/boundary.hpp	Added bounding box infrastructure for ghost regions
test/MHD/AmbipolarCshock3D/*.{cpp,ini}	Updated test setup: fixed vector potential initialization and changed boundary conditions
test/MHD/AmbipolarCshock3D/testme.py	Relaxed tolerance from 2e-14 to 3e-14
test/MHD/ShearingBox/testme.py	Added MPI test coverage

Comments suppressed due to low confidence (2)

test/MHD/AmbipolarCshock3D/testme.py:1

• The tolerance was relaxed from 2e-14 to 3e-14. While this may be necessary due to the new MPI exchange logic, ensure that this increased tolerance does not mask potential numerical accuracy issues. Consider documenting why this change was needed.
  test/MHD/AmbipolarCshock3D/setup.cpp:1
• This debug output line is very long. Consider breaking it into multiple lines for better readability, or using formatted output with appropriate field widths.

#include "idefix.hpp"

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