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Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Nuclear Science and Technology Taylor & Francis

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

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References (27)

Publisher
Taylor & Francis
Copyright
© 2024 Atomic Energy Society of Japan. All rights reserved.
ISSN
0022-3131
eISSN
1881-1248
DOI
10.1080/00223131.2024.2365445
Publisher site
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Abstract

In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.

Journal

Journal of Nuclear Science and Technology – Taylor & Francis

Published: Dec 1, 2024

Keywords: Proper orthogonal decomposition; dimensionality reduction; tally method; Monte Carlo calculation; multi-group calculation; numerical simulation; verification

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