Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

TL;DR

This paper introduces Poisson-Box Sampling algorithms to improve the accuracy of particle transport simulations in three-dimensional Markov binary mixtures, outperforming traditional Chord Length Sampling methods with manageable computational costs.

Contribution

The paper proposes a novel Poisson-Box Sampling approach that enhances the accuracy of CLS algorithms for 3D Markov media in particle transport simulations.

Findings

PBS outperforms CLS in accuracy for scalar flux, transmission, and reflection.

PBS achieves this with a reasonable increase in computational time.

Benchmark tests confirm the improved performance of PBS over CLS.

Abstract

Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in $d$-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning and extended by Brantley: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.