Benchmark Solutions For Transport In $d$-Dimensional Markov Binary Mixtures
Résumé
Particle transport in random media obeying a given mixing statistics is key in several applications innuclear reactor physics and more generally in diusion phenomena emerging in physics and life sciences. Exactsolutions for the ensemble-averaged physical observables are hardly available, and several eective modelshave been thus developed, providing a compromise between the accurate treatment of the disorder-inducedspatial correlations and the computational time. In order to validate these models, it is mandatory to resort toreference solutions. We extend the pioneering work by Adams, Larsen and Pomraning (recently revisited byBrantley [2]) by considering a series of benchmark configurations for mono-energetic and isotropic transportthrough Markov binary mixtures in dimension d. The stochastic media are generated by resorting to Poissonrandom tessellations in 1$d\ slab$, 2$d$ extruded, and full 3$d$ geometry. For each realization, particle transportis performed by resorting to Monte Carlo simulation. The distributions of the transmission and reflectioncoecients on the free surfaces of the geometry are subsequently estimated, and the average values over theensemble of realizations are computed. Reference solutions for the benchmark have never been provided beforefor two- and three-dimensional Poisson tessellations, and the results presented in this paper might thus beuseful in order to validate fast but approximated models for particle transport in Markov stochastic media,such as the celebrated Chord Length Sampling algorithm.
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