An adaptive reduced order model for the angular discretization of the Boltzmann transport equation using independent basis sets over a partitioning of the space-angle domain

This article presents a new reduced order model (ROM) for the angular discretization of the Boltzmann transport equation. The angular ROM is built over a partitioning of the space-angle phase-space, by generating independent, optimized angular basis function sets for each partition. The advantage is that each basis function set is optimized to represent the neutron flux distribution in a particular partition of space and angle, rather than being optimized for the entire domain. This serves to reduce the total number of basis functions required, and therefore the solve time. Two numerical examples are presented to demonstrate the efficacy of the methods-a dog-leg duct problem, involving particle streaming, and the Watanabe-Maynard problem, which includes significant particle scattering. In both cases, it is shown that the method reduces the angular flux error, for a given basis size or solve time, by around an order of magnitude in comparison to other, similar ROM methods. An adaptive version of the method is also presented, whereby the number of basis functions within each space-angle partition can vary independently. It is shown to potentially provide further significant reductions in error.