Stability diagnosis of high-fidelity transport-depletion problems with Monte Carlo perturbation theory

P. Cosgrove, E. Shwageraus, G. T. Parks

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Obtaining a stable solution with coupled neutron transport and isotopic depletion has been cast as a non-linear root-finding problem by focusing on the corrector step of the standard predictor-corrector algorithm. This allows a Jacobian matrix to be defined, relating the isotopic field at one iteration to the isotopic field at the previous iteration. The spectral radius of the Jacobian defines the stability of the coupled system. Using perturbation theory, the Jacobian has been calculated for a PWR pin undergoing burn-up – with and without xenon equilibriation – and its numerical stability is examined. The results suggest that PWR pins with uniform coolant density are in fact numerically stable – observed instabilities result purely from statistical effects in the Monte Carlo solver.

Original languageEnglish
Title of host publicationInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019
PublisherAmerican Nuclear Society
Pages1154-1163
Number of pages10
ISBN (Electronic)9780894487699
StatePublished - 1 Jan 2019
Externally publishedYes
Event2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019 - Portland, United States
Duration: 25 Aug 201929 Aug 2019

Publication series

NameInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019

Conference

Conference2019 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019
Country/TerritoryUnited States
CityPortland
Period25/08/1929/08/19

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