Fix upwind/downwind finite volume operators

[brosaplanella]

Description

Fixed the issue with the upwind and downwind operators. I am now leveraging the add_ghost_nodes method, to which I had to do some minor changes.

Fixes #3526

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #) - note reverse order of PR #s. If necessary, also add to the list of breaking changes.

• New feature (non-breaking change which adds functionality)
• Optimization (back-end change that speeds up the code)
• Bug fix (non-breaking change which fixes an issue)

Key checklist:

• No style issues: $ pre-commit run (or $ nox -s pre-commit) (see CONTRIBUTING.md for how to set this up to run automatically when committing locally, in just two lines of code)
• All tests pass: $ python run-tests.py --all (or $ nox -s tests)
• The documentation builds: $ python run-tests.py --doctest (or $ nox -s doctests)

You can run integration tests, unit tests, and doctests together at once, using $ python run-tests.py --quick (or $ nox -s quick).

Further checks:

• Code is commented, particularly in hard-to-understand areas
• Tests added that prove fix is effective or that feature works

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.58%. Comparing base (4cf09f3) to head (d57c0d7).

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Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #3979      +/-   ##
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- Coverage    99.58%   99.58%   -0.01%     
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  Files          257      257              
  Lines        21254    21248       -6     
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- Hits         21166    21160       -6     
  Misses          88       88              

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[valentinsulzer]

Thanks, looks good. Can you show plots of the upwinding example vs analytical solution before and after the fix?

[brosaplanella]

Before & after plots

$$ u_t + u_x = s, \quad 0 < x < 1$$

$$u(t,0) = b$$

$$u(0,x) = 0$$

Example 1

s = 1, b = 0

Before

After

Example 2

s = 0, b = 1

Before

After

[valentinsulzer]

Thanks, that does look much better! Is the mismatch with the analytical solution because it's not a high-enough order scheme?

[brosaplanella]

I think so, as refining the mesh gives a better result. I need to do some more reading on this, and potentially implement higher order methods, but that's a separate issue.