For Poisson and Poisson-Box tessellations, a ‘coloring’ procedure is performed after the sampling of the cells of the skeleton geometry [2, 3]: each cell of the tessellation is assigned a color label 'c' with a probability p(c) , c = 1, …, n. The resulting stochastic configurations form isotropic or anisotropic random n-ary Markov mixtures (collections of material compositions whose geometrical shapes obey a given probability distribution), and provide convenient models to describe complex systems such as corium following severe accidents, or turbulent layers in fusion pellets [4].
For spherical inclusions, binary mixtures result from the sampling (the sphere and the background matrix), with a given packing fraction: such configurations might be used e.g. to model the fuel elements of HTR reactors [5]. Two models are available: either the Random Sequential Addition (RSA) with mesh-based acceleration, or the Jodrey-Tory (JT) algorithm.
For each of the available random media models, CASTOR samples an ensemble of M realizations, compatible with the format expected by TRIPOLI-4 (including the geometry, the boundary conditions, and the association between cells and material compositions). For each realization, a TRIPOLI-4 simulation is run and a set of observables is estimated. The histogram over the set of performed simulations allows computing the average and the dispersion of the sought results (the dispersion is due to both the variance of the underlying stochastic media and the statistical dispersion of the Monte Carlo simulations). Reference solutions for particle transport computed by taking an ensemble over a large collection of random media realizations can be used to benchmark results obtained with faster-homogenized models such as the Chord Length Sampling method [6-7].