Distribution of porosity

[Rombur]

Look at the physical effect of having a distribution for the porosity: use a constant-per-cell porosity. Hopefully, we should get the right slope on the Nyquist plot.

[dalg24]

PR #192 on ORNL-CEES/Cap implements inhomogeneous material properties.

Here is how to modify the super capacitor property tree to use it.

material_properties {
  [...]
  inhomogeneous true
  parameters 2
  parameter_0 {
    path separator_material.void_volume_fraction
    distribution_type uniform
    range 0.55,0.65
  }
  parameter_1 {
    path electrode_material.void_volume_fraction
    distribution_type normal
    mean 0.67
    standard_deviation 0.04
  }
}

[dalg24]

PR #184 which has already been merged enabled to specify the frequencies for an electrochemical impedance spectroscopy experiment. It is useful to compare experimental versus computed spectra.

PR #198 demonstrate how to use it. It comes with an experimental spectrum and more importantly propose a mathematical criterion to tell how much two spectra agree.

[dalg24]

Paragraphs:

• 2D/3D impedance spectroscopy with refinement check convergence
• comparison 2D/3D
• polynomial chaos on homogeneous domain
• comparison with experiment

[dalg24]

Starting with

  parameters 2
  parameter_0 {
    path separator_material.void_volume_fraction
    distribution_type uniform
    range 0.55,0.65
  }
  parameter_1 {
    path electrode_material.void_volume_fraction
    distribution_type uniform
    range 0.62,0.72
  }

[Rombur]

After talking with Frank, here is the scope of the paper has been changed. The goal is now to show the capabilities of the code and advertise how, by adding more realistic physics, the code should be able to answer questions that cannot be answered by 1D models. The structure of the paper will be:

• description of the mathematical model used
• use a distribution of properties in the material, use the a gradient of variation in the material. Because the goal is to show capabilities, the distribution does not need to be realistic
• use of a complex 3D geometry. Having one electrode and the separator using the following geometry http://dealii.org/8.4.1/doxygen/deal.II/namespaceGridGenerator.html#a6909eec7b1bee57374d52a9dfe240d57