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

Abstract

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.

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…In recent years, many data-driven ROMs have been developed using these techniques for linear problems involving the BTE. Dimensionality reduction in the angular variable has been formulated using both the POD and reduced-basis methods [43,44,45,46,47]. POD-Petrov-Galerkin projections have been formulated for the steady-state BTE in 1D geometry [48,49].…”

“…A new approach based on data-driven reduced-order models (ROMs) has been gaining popularity in recent years which make use of data-based methodologies to dimensionality reduction. Data-driven models have been developed for (i) linear particle transport problems [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (ii) nonlinear RT problems [49,50,51,52,53,54,55,56,57,58,59,60], and (iii) various problems in nuclear reactor-physics [61,62,63,64,65,66,67,68,69,70,71]. The fundamental idea behind these ROMs is to leverage databases of solutions to their problems of interest (known a-priori) to develop some reduction in the dimensionality for their involved equations.…”