Implementation of migration area score

[GuySten]

Description

This PR implement 'migration-area' score to calculate diffusion coefficients and transport cross sections for multigroup.

Fixes #1734

Theory

https://www.researchgate.net/publication/324831861_Group-wise_Tally_Scheme_of_Incremental_Migration_Area_for_Cumulative_Migration_Method

Example

import openmc
import matplotlib.pyplot as plt

model = openmc.Model()

# Material
material = openmc.Material(name="Hydrogen")
material.add_nuclide("H1", 1.0)
material.set_density('g/cm3', 1.0)
material.add_s_alpha_beta('c_H_in_H2O')

# Geometry
radius = 10.0
sphere = openmc.Sphere(r=radius, boundary_type="reflective")
cell = openmc.Cell(region=-sphere, fill=material)
model.geometry = openmc.Geometry([cell])

# Settings
model.settings.particles = 100000
model.settings.batches = 20
model.settings.run_mode = 'fixed source'
model.settings.source = openmc.IndependentSource()
    

# Tally 
groups = openmc.mgxs.EnergyGroups('CASMO-70')
energy_filter = openmc.EnergyFilter(groups.group_edges)
tally = openmc.Tally()
tally.scores = ["migration-area", "flux", "total"]
tally.filters = [energy_filter]
model.tallies = [tally]

model.run()


with openmc.StatePoint('statepoint.20.h5') as sp:
    tally = sp.get_tally(id=1)
    
energies = 0.5*(groups.group_edges[1:]+groups.group_edges[:-1])
flux =  tally.get_values(value='mean', scores=['flux']).squeeze()
total =  tally.get_values(value='mean', scores=['total']).squeeze()
migration_area = tally.get_values(value='mean', scores=['migration-area']).squeeze()

migration_area /= flux
total /= flux

plt.semilogx(energies,1/(3*migration_area*total))
plt.title(r'$\Sigma_{tr}/\Sigma_t$')
plt.show()

Reference results:

Checklist

• I have performed a self-review of my own code
• I have run clang-format (version 15) on any C++ source files (if applicable)
• I have followed the style guidelines for Python source files (if applicable)
• I have made corresponding changes to the documentation (if applicable)
• I have added tests that prove my fix is effective or that my feature works (if applicable)

[GiudGiud]

Thanks for the PR!

[GiudGiud]

this global variable is justifiable because we need it during the simulation at every BC

[GiudGiud]

this one is not, it's a setup item it should be handled with a check over all surfaces not the setting of a global boolean

[GuySten]

This variable is set when reading surfaces and used when setting tallies.
So removing it will involve alot of function signature change.
I think this way is better.

[GiudGiud]

you would just need to not set it when reading surfaces, then when setting tallies you can loop over the geometry/surfaces if migration tallies are used to check their type

[GuySten]

In general it is not recommended to iterate over cells or surfaces twice because there are models with alot of cells and surfaces.

[GuySten]

@paulromano, what do you think?

This issue can affect performance.

[GiudGiud]

is this test case the one used for the figures? If so let's keep it, we somewhat know what the result looks like

But we also need coverage on all the other types of supported boundary conditions. So let's make either:

• a dummy test featuring all these
  or better:
• a test featuring these BCs but that gives the exact same result due to the symmetries of the geometry

[GuySten]

The current regression test is the same one from the example.

I've added a test that a large water sphere gives the same results as a small one with reflective boundary conditions.

I think I know how to extend this PR to white boundary conditions but I will leave that as a potential future PR.

[GiudGiud]

I think I know how to extend this PR to white boundary conditions but I will leave that as a potential future PR.

Yes for sure.
If OpenMC testing involves exception testing we'll just want a test that shows the error.
@paulromano might give guidance on whether it's needed here

[GiudGiud]

@GuySten you should be able to lump the suggestions from the files tab (cant do it from the conversation tab) to limit the test suite runs (for next time)