A reduced order model discretisation of the space-angle phase-space dimensions of the Boltzmann transport equation with application to nuclear reactor problems

Abstract

This article presents a new reduced order model (ROM) for fast solutions to neutron transport problems. The novelty lies in the construction of optimal basis functions spanning the space-angle phase-space dimensions of the Boltzmann transport equation (BTE). It uses Proper Orthogonal Decomposition and the method of snapshots to form the reduced basis, but here a 2-stage construction is proposed that compresses the angle, then space, dimensions sequentially. The approach alleviates the potentially limiting memory burden for BTE-based ROMs by not processing the full discretised solutions of BTE during the construction stage. The model is both accurate and efficient and is demonstrated here for eigenvalue and fixed source reactor physics problems with assumed uncertainties in material cross-section data. Reductions in problem size and solving times exceeds 5 orders of magnitude in comparison to high fidelity models, and which could potentially improve further for larger scale problems.