Fix issues with history output

[michelebucelli]

Fixes #615 about incorrect reporting of iterations in multi-equation simulations. Also adds some cosmetic improvements to the history table. See the issue for details.

This has no effect on calculations, but only on convergence history reporting.

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[claude]

Claude Code Review

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[Copilot]

Pull request overview

This PR addresses incorrect convergence history reporting in multi-equation simulations (Fixes #615) by restructuring when/where history rows are emitted, and by reformatting the history table for consistent fixed-width alignment.

Changes:

• Introduce output::output_header() and refactor output::output_result() to generate aligned, fixed-width history output (including improved separator handling).
• Move history row emission into Integrator::step() so every Newton iteration (including the converged one) is printed exactly once, with an s flag when VTU output is scheduled.
• Simplify VTU-save decision logic in main.cpp and pass it into Integrator::step(save_vtu).

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
Code/Source/solver/output.h	Adds output_header() and updates output_result() API/documentation.
Code/Source/solver/output.cpp	Implements header printing + fixed-width row formatting and separator generation.
Code/Source/solver/main.cpp	Computes save_vtu, passes it to Integrator::step(), and streamlines VTU write logic.
Code/Source/solver/Integrator.h	Extends step() signature to accept save_results flag (defaulted).
Code/Source/solver/Integrator.cpp	Emits one history row per Newton iteration (including converged) from within step().
Code/Source/solver/initialize.cpp	Switches history initialization from output_result(co=1) to output_header().

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 72.86%. Comparing base (9ff6e43) to head (a7b4688).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #624   +/-   ##
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  Coverage   72.86%   72.86%           
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  Files         258      258           
  Lines       39500    39490   -10     
  Branches     6730     6726    -4     
=======================================
- Hits        28780    28773    -7     
+ Misses      10477    10474    -3     
  Partials      243      243           

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[zasexton]

This looks good to me

[kko27]

Thanks so much @michelebucelli! The changes look great! Have two minor comments.

[kko27]

Is there a possibility of also replacing these boolean flags with more meaningful variable names, or removing them? Not sure if that increases the scope of this PR.

[michelebucelli]

Done, as follows:

1. l1 was only used in a statement like l1 = expression_A; if (expression_B && l1) { ... }. I removed the variable l1 entirely, and replaced that statement with if (expression_B && expression_A) { ... }. Since the two expressions were slightly obscure due to the variables involved having somewhat cryptic names (to me at least), I included comments to explain the meaning of both (I'd rather not go on a variable renaming spree at this time 😅 ).
2. l2 was used similarly, although its value was printed by a debug statement as well so it couldn't be removed without changing behavior. I moved its declaration down to where it is used, and gave it the more explicit name is_restart_output_step.
3. There was another l1 variable, declared in the while loop (and thus hiding the l1 variable here). I also renamed it to reached_stop_time_step.

Conceivably there's a bit more cleanup to be done in the main function code along these lines (making variables as local as possible, giving more expressive names, removing unused variables), but maybe we can save it for a more scoped issue.