Variational processing of stochastic simulation in neutron transport: the three-dimensional system

The variational processing of Monte Carlo results in a two-group in®nite homogeneous multiplying system, one-dimensional scattering and neutron deep penetration problems improved the accuracy and reduced the variance of the analogue Monte Carlo estimates, especially when virtual sampling was utilized. In this paper, the use of virtual sampling in variational processing of Monte Carlo solutions to a more realistic three-dimensional problem is addressed. The results of this study are in agreement with the results of previous papers. The analytical solutions of this model are obtained by Neumann iterative method for di€erent values of scattering ratios and for di€erent cell widths. The importance functions used in the variational processing are ®rst obtained by ®ctitious sampling and then by the virtual sam- pling technique. Both show a signi®cant reduction in variance and in percentage di€erence from the exact results. The overall performance, however, favours the use of virtual sampling. As in previous cases, correlation e€ects were found to be advantageous for the cases con- sidered. The convergence of the variationally processed Monte Carlo is found to obey approximately the Lewins conjecture: a 1=N2 behaviour rather than the 1=N for the analogue Monte Carlo.