14. Stochastic Volume Calculations

OpenMC has a capability to stochastically determine volumes of cells, materials, and universes. The method works by overlaying a bounding box, sampling points from within the box, and seeing what fraction of points were found in a desired domain. The benefit of doing this stochastically (as opposed to equally-spaced points), is that it is possible to give reliable error estimates on each stochastic quantity.

To specify that a volume calculation be run, you first need to create an instance of openmc.VolumeCalculation. The constructor takes a list of cells, materials, or universes; the number of samples to be used; and the lower-left and upper-right Cartesian coordinates of a bounding box that encloses the specified domains:

lower_left = (-0.62, -0.62, -50.)
upper_right = (0.62, 0.62, 50.)
vol_calc = openmc.VolumeCalculation([fuel, clad, moderator], 1000000,
                                    lower_left, upper_right)

For domains contained within regions that have simple definitions, OpenMC can sometimes automatically determine a bounding box. In this case, the last two arguments are not necessary. For example,

sphere = openmc.Sphere(r=10.0)
cell = openm.Cell(region=-sphere)
vol_calc = openmc.VolumeCalculation([cell], 1000000)

Of course, the volumes that you need this capability for are often the ones with complex definitions.

A threshold can be applied for the calculation’s variance, standard deviation, or relative error of volume estimates using openmc.VolumeCalculation.set_trigger():

vol_calc.set_trigger(1e-05, 'std_dev')

If a threshold is provided, calculations will be performed iteratively using the number of samples specified on the calculation until all volume uncertainties are below the threshold value. If no threshold is provided, the calculation will run the number of samples specified once and return the result.

Once you have one or more openmc.VolumeCalculation objects created, you can then assign then to Settings.volume_calculations:

settings = openmc.Settings()
settings.volume_calculations = [cell_vol_calc, mat_vol_calc]

To execute the volume calculations, one can either set Settings.run_mode to ‘volume’ and run openmc.run(), or alternatively run openmc.calculate_volumes() which doesn’t require that Settings.run_mode be set.

When your volume calculations have finished, you can load the results using the VolumeCalculation.load_results() method on an existing object. If you don’t have an existing VolumeCalculation object, you can create one and load results simultaneously using the VolumeCalculation.from_hdf5() class method:

vol_calc = openmc.VolumeCalculation(...)

# ..or we can create a new object
vol_calc = openmc.VolumeCalculation.from_hdf5('volume_1.h5')

After the results are loaded, volume estimates will be stored in VolumeCalculation.volumes. There is also a VolumeCalculation.atoms_dataframe attribute that shows stochastic estimates of the number of atoms of each type of nuclide within the specified domains along with their uncertainties.