add temperature dependence to MSMR model

[valentinsulzer]

Description

The FR/T term now uses the appropriate local temperature. Individual parameters (x_j, U0_j, w_j, alpha_j) can also depend on temperature, but this isn't tested. Plett Volume 3 claims that those parameters should not change much as a function of temperature.

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 99.54%. Comparing base (afbf21d) to head (81dc161).

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #3832      +/-   ##
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- Coverage    99.59%   99.54%   -0.05%     
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  Files          287      287              
  Lines        21723    21744      +21     
===========================================
+ Hits         21635    21646      +11     
- Misses          88       98      +10     

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[rtimms]

Thanks, looks good, just a couple of things to tidy up.

We should make it clear in the docs/example how dUdT is used in the MSMR model. In the "standard" model U(x,T) = U_ref(x) + (T-T_ref)*dUdT whereas here U(x,T) is solved for explicitly, and dUdT is just used to calculate the reversible heat term.

[valentinsulzer]

Where would you clarify the dU/dT thing in the docs?

[rtimms]

Where would you clarify the dU/dT thing in the docs?

I think there are 3 places where it is relevant: the definition of U in LithiumIonParameters, the definition of dUdT in LithiumIonParameters and in the submodel for MSMR where you solve for U. Probably makes most sense to put in dUdT and then crossref?

[brosaplanella]

Happy to merge this one once the conflicts are resolved. There are also some coverage issues, but the detailed report does not load, so it might be a Codecov artifact.