Memory-preserving Chord Length Sampling in three-dimensional spatially heterogeneous Markov media: Preliminary investigations

Abstract

We report on an investigation of particle transport in spatially heterogeneous Markov media using a memory-preserving Chord Length Sampling (CLS) algorithm. CLS are a family of Monte Carlo methods capable of generating approximate solutions of the transport equations in random geometries by generating material interfaces on-the-fly during particle propagation. Since CLS does not preserve the correlations induced by spatial disorder, the sampled solutions generally present discrepancies with respect to the reference solution obtained by solving the Boltzmann equation in a large ensemble of random media realizations. In order to increase the accuracy of CLS, improved CLS models endowed with spatial memory effects have been proposed. In this work we propose a strategy that allows simultaneously taking into account memory effects and spatial gradients in three-dimensional configurations. Preliminary numerical findings are illustrated and compared to reference solutions.