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)