Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

Abstract

Producing high-fidelity real-time simulations of neutron diffusion in a reactor is computationally extremely challenging, due, in part, to multiscale behaviour in energy and space. In many scientific fields, including nuclear modelling, the application of reduced-order modelling can lead to much faster computation times without much loss of accuracy, paving the way for real-time simulation as well as multi-query problems such as uncertainty quantification and data assimilation. This paper compares two reduced-order models that are applied to model the movement of control rods in a fuel assembly for a given temperature profile. The first is a standard approach using proper orthogonal decomposition (POD) to generate global basis functions, and the second, a new method, uses POD but produces global basis functions that are local in the parameter space (associated with the control-rod height). To approximate the eigenvalue problem in reduced space, a novel, nonlinear interpolation is proposed for modelling dependence on the control-rod height. This is seen to improve the accuracy in the predictions of both methods for unseen parameter values by two orders of magnitude for keff and by one order of magnitude for the scalar flux.

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

“…More recently, POD has been used to model fuel burnup 36 and reactor power distributions 37 . Many articles have also considered the problem of control rod movement using various ROMs, including early work based on proper generalized decomposition, 38 and recent publications which employed POD, 39 the empirical interpolation method, 40 and neural networks 41 …”

“…35 More recently, POD has been used to model fuel burnup 36 and reactor power distributions. 37 Many articles have also considered the problem of control rod movement using various ROMs, including early work based on proper generalized decomposition, 38 and recent publications which employed POD, 39 the empirical interpolation method, 40 and neural networks. 41 Recently, a new adaptive POD method known as discontinuous POD (DPOD) was developed, which applied angular POD functions to optimally resolve the angular dimension of the BTE over distinct partitions of the angular domain.…”

Fixed Assets Positioning Management Based on Nonlinear Difference Algorithm

“…However, the existing interpolation algorithms ignore the effect of the nonlinear variation of the radio frequency signal on the interpolation accuracy, resulting in low interpolation accuracy. To this end, many scholars have proposed a variety of sensor nonlinear compensation methods [13,14]. en, the signal feature quantity does not conform to the linear distribution due to a complex environment or a large distance between acquisition points; the nonlinear interpolation algorithm can be used to accurately calculate the signal feature statistics between the points according to the nonlinear distribution law, allowing the location of the anchor point to be determined.…”

Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

“…Heaney et al [11] applied a POD-based ROM to a PWR fuel assembly in order to model control-rod movement and temperature. This method was further extended to use basis functions that were local in the parameter space [12]. In both [11] and [12], different sets of POD basis functions were produced for each energy group, a method demonstrated by German and Ragusa [13] to be more robust than a monolithic approach, which produced POD basis functions across all energy groups simultaneously.…”

“…This method was further extended to use basis functions that were local in the parameter space [12]. In both [11] and [12], different sets of POD basis functions were produced for each energy group, a method demonstrated by German and Ragusa [13] to be more robust than a monolithic approach, which produced POD basis functions across all energy groups simultaneously. Sartori et al [14] developed a reduced basis approach to model control rod movement for the TRIGA Mark II reactor core.…”