Monte Carlo Chord Length Sampling for d-dimensional Markov binary mixtures

International audienceThe Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media onparticle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This an-nealed disorder approach, which formally consists of solving the approximate Levermore-Pomraning equations for linear particletransport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltz-mann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced bythe spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respectto reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, suchcomparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extendthese results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set ofbenchmark configurations originally proposed by Adams, Larsen and Pomraning (1) and extended by Brantley (2). In particular,we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission-reflection coefficientsas a function of the material properties of the benchmark specifications and of the system dimensionality