Benchmark results for particle transport in a binary Markov statistical medium

Abstract

We give numerical benchmark results for particle transport in a randomly mixed binary medium, with the mixing statistics described as a homogeneous Markov process. A Monte Carlo procedure is used to generate a physical realization of the statistics, and a discrete ordinate numerical transport solution is generated for this realization. The ensemble averaged solution, as well as the variance, is obtained by averaging a large number of such calculations. Reflection and transmission results are given for several problems in both rod and planar geometry. In a separate development, two coupled transport equations are derived which formally describe transport in a random binary mixture for arbitrary mixing statistics. Closing these equations by approximating their coupling terms in a low order and intuitive way leads to a model for stochastic transport previously obtained via the master equation. The present derivation, based upon approximating exact equations, allows in principle the opportunity to develop more accurate models by making higher order approximations in the coupling terms.

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

“…Zuchuat, Sanchez, Zmijarevic, and Malvagi [6] reproduced the Markovian statistics benchmark results published in Ref. [5] and extended these benchmark solutions to additional non-Markovian material statistics. In addition to the reflection and transmission values, Zuchuat et al compared the ensemble-averaged total and material scalar flux distributions.…”

“…We consider the following two time-independent monoenergetic neutron transport problems [5,12] with isotropic scattering in a one-dimensional planar geometry spatial domain defined on 0 ≤ x ≤ L:…”

“…The accuracy of the Levermore-Pomraning model has previously been examined by Adams, Larsen, and Pomraning [5] using a suite of benchmark problems involving a non-stochastic isotropic angular flux incident on one boundary of a one-dimensional planar geometry binary stochastic medium. The benchmark suite is characterized by nine different sets of material cross sections, mean material slab widths, and material scattering ratios as well as three different total slab widths.…”

“…Zimmerman and Adams [2] numerically demonstrated that the base Monte Carlo algorithm (Algorithm A) solves the Levermore-Pomraning equations and that the improved algorithm (Algorithm B) is more accurate by comparing the results of these algorithms to the standard suite (Suite I) of planar geometry incident angular flux binary stochastic mixture benchmark transport solutions [5]. In this paper, we extend the incident angular flux benchmark comparisons of these Monte Carlo algorithms to include the ensemble-averaged material scalar flux distributions produced.…”

“…The numerical solutions to both benchmark suites were obtained using the Monte Carlo procedures described by Adams et al [5] and Zuchuat et al [6] in which independent material realizations are sampled from the Markovian statistics and the transport problem is solved for each realization using the discrete ordinates transport method [14] and a high-order angular quadrature set. 5 × 10 5 independent realizations were simulated and the results averaged to obtain ensemble-averaged values for the leakage from the slab.…”