Particle transport in Markov media with spatial gradients: Comparison between reference solutions and Chord Length Sampling

Abstract

Markov media represent a prototype class of stochastic models that are commonly used to describe the statistical distribution of material properties for particle transport applications. Examples are widespread and emerge for instance in radiative transfer or neutron propagation through disordered materials. Particle transport in Markov media can be addressed by two distinct strategies. The first consists in sampling a collection of stochastic geometries, solving the Boltzmann equation for each realisation, and finally taking ensemble averages, which leads to reference solutions for the observables of interest at the expense of high computational cost. The second consists in developing faster but approximate transport models capable of mimicking the effects of disorder within a single transport calculation, such as the celebrated Levermore-Pomraning (LP) equations and their Monte Carlo counterpart, the Chord Length Sampling (CLS) model. In this work we address particle transport in three-dimensional Markov media displaying spatial gradients in their statistical properties, and we compare the CLS model and SN solutions of the LP equations to the reference solutions.