Monte Carlo Methods for the Neutron Transport Equation
Alexander M. G. Cox, Simon C. Harris, Andreas E. Kyprianou, Minmin Wang
Abstract
This paper continues our treatment of the Neutron Transport Equation (NTE) building on the work in [13], [28] and [25], which describes the density (equiv. flux) of neutrons through inhomogeneous fissile medium. Our aim is to analyse existing and novel Monte Carlo (MC) algorithms, aimed at simu- lating the lead eigenvalue associated with the underlying model. This quantity is of principal importance in the nuclear regula- tory industry for which the NTE must be solved on complicated inhomogenous domains corresponding to nuclear reactor cores, irradiative hospital equipment, food irradiation equipment and so on. We include a complexity analysis of such MC algorithms, noting that no such undertaking has previously appeared in the literature. The new MC algorithms offer a variety of advantages and disadvantages of accuracy vs cost, as well as the possibility of more convenient computational parallelisation.