Acceleration techniques for trajectory-based deterministic 3D transport solvers

摘要

In this paper, we present new acceleration techniques for solving the linear transport equation in general 3D unstructured domains with isotropic boundary conditions. First, a track merging algorithm is used to consistently gather trajectories crossing similar regions. This domain-decomposition algorithm uses the generic geometrical concept of 3D micro-bands, where trajectories are classified by subsets of their region-crossing numbers. Secondly, a new local rebalancing technique is used to reduce the total number of iterations for multi-group calculations.This technique uses the self-collision probabilities of every spatial region to perform local group rebalancing. Based on approximations similar to the usual interface-current formalism, the out-going boundary currents are adjusted according to the rebalanced fluxes. Assuming isotropic sources and scattering, both techniques needs little programming effort and can be implemented into any characteristics or collision-probability solver. The main advantage of these techniques is that they are not memory intensive, requiring only new arrays of the size of the multigroup flux. Numerical comparisons show the accuracy of these algorithms for 3D supercells in a CANDU reactor. These algorithms were found particularly useful for speeding up transport calculations with high-scattering ratios.