Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures
Résumé
Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of MonteCarlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the materialinterfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computationalresources with respect to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions are faster albeit approximate, since correlations induced by the spatial disorder are ignored, and mightthus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called -PoissonBox Sampling-, PBS) aimed at improving the accuracy of the CLS approach for transport in d-dimensional binary Markov geometries. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmarkproblem originally proposed by Adams, Larsen and Pomraning (1) and extended by Brantley (2) for these configurations we willcompare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflectioncoefficients. BBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.
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