A “two-grid” acceleration of binary stochastic mixture deterministic transport iterations in slab geometry

Abstract

Particle transport in stochastic mixtures has been an area of active research during the last decade. The primary focus has been on the development of simple, efficient models that approximate the behavior of transport solutions which have been ensemble-averaged over a large number of realizations of the mixing statistics. These approximate models are often written as coupled systems of transport equations. The stochastic nature of this problem can be naturally incorporated into Monte Carlo transport codes, but there have also been efforts to solve these coupled equations deterministically. In this paper, we develop an efficient iterative technique for the deterministic solution of the coupled transport equations of the Levermore–Pomraning mix model. The basis for its development is the observation that these equations are similar in structure to traditional multigroup transport equations with upscattering. We provide the results of a Fourier analysis of this technique, and compare these with observed convergence rates from the implemented algorithm.