Pass R(x) directly for graded electrodes

[rtimms]

Description

The parameters "Positive/Negative particle distribution in x" and "Positive/Negative surface area per unit volume distribution in x" have been deprecated. Instead, users can provide "Positive/Negative particle radius [m]" and "Positive/Negative surface area per unit volume [m-1]" directly as functions of through-cell position (x [m])

The parameters related to this (in LithiumIonParameters and LeadAcidParameters) are now defined as follows:

R_n_dimensional(x) the dimensional particle radius in the negative electrode as a function of dimensional through-cell position
R_p_dimensional(x) the dimensional particle radius in the positive electrode as a function of dimensional through-cell position
a_n_dimensional(x) the dimensional surface area per unit volume in the negative electrode as a function of dimensional through-cell position
a_p_dimensional(x) the dimensional surface area per unit volume in the positive electrode as a function of dimensional through-cell position
R_n_typ the typical radius in the negative electrode (taken to be the radius at the electrode/current collector interface)
R_p_typ the typical radius in the positive electrode (taken to be the radius at the electrode/current collector interface)
a_n_typ the typical surface area per unit volume in the negative electrode (taken to be the radius at the electrode/current collector interface)
a_p_typ the typical surface area per unit volume in the positive electrode (taken to be the radius at the electrode/current collector interface)
a_R_n the product of typical surface area per unit volume and typical radius in the negative electrode (dimensionless)
a_R_p the product of typical surface area per unit volume and typical radius in the positive electrode (dimensionless)
R_n(x) the dimensionless particle radius in the negative electrode as a function of dimensionless through-cell position
R_p(x) the dimensionless particle radius in the positive electrode as a function of dimensionless through-cell position
a_n(x) the dimensionless surface area per unit volume in the negative electrode as a function of dimensionless through-cell position
a_p(x) the dimensionless surface area per unit volume in the positive electrode as a function of dimensionless through-cell position

The last four are equal to unity for uniform radius/surface area per unit volume.

Fixes #1236

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: $ flake8
• All tests pass: $ python run-tests.py --unit
• The documentation builds: $ cd docs and then $ make clean; make html

You can run all three at once, using $ python run-tests.py --quick.

Further checks:

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

[codecov]

Codecov Report

Merging #1237 (9731e57) into develop (2d57749) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff            @@
##           develop    #1237   +/-   ##
========================================
  Coverage    97.95%   97.96%           
========================================
  Files          250      250           
  Lines        14397    14423   +26     
========================================
+ Hits         14103    14129   +26     
  Misses         294      294           

Impacted Files	Coverage Δ
...ttery_models/lithium_ion/base_lithium_ion_model.py	100.00% <ø> (ø)
...odels/full_battery_models/lithium_ion/basic_dfn.py	100.00% <ø> (ø)
...odels/full_battery_models/lithium_ion/basic_spm.py	100.00% <ø> (ø)
...dels/submodels/particle/fickian_single_particle.py	100.00% <ø> (ø)
pybamm/parameters/geometric_parameters.py	100.00% <ø> (ø)
...m/models/full_battery_models/base_battery_model.py	99.67% <100.00%> (ø)
..._battery_models/lithium_ion/basic_dfn_half_cell.py	99.21% <100.00%> (ø)
pybamm/models/submodels/electrode/ohm/full_ohm.py	100.00% <100.00%> (ø)
...dels/electrolyte_conductivity/full_conductivity.py	100.00% <100.00%> (ø)
...e_potential_form/full_surface_form_conductivity.py	100.00% <100.00%> (ø)
... and 10 more

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 2d57749...2a35655. Read the comment docs.

[brosaplanella]

Looks good, thanks Rob!

[valentinsulzer]

Looks good to me, thanks!