Application of proper generalized decomposition to multigroup neutron diffusion eigenvalue calculations

Prince, Zachary M.; Ragusa, Jean C.

doi:10.1016/j.pnucene.2019.103232

Title: Application of proper generalized decomposition to multigroup neutron diffusion eigenvalue calculations

Journal Article · 10 January 2020 · Progress in Nuclear Energy

DOI: https://doi.org/10.1016/j.pnucene.2019.103232 · OSTI ID:1801174

Prince, Zachary M. ^[1]; Ragusa, Jean C. ^[2]

Texas A & M Univ., College Station, TX (United States); OSTI
Texas A & M Univ., College Station, TX (United States)

In this work, proper generalized decomposition (PGD) is utilized to reduce the computational burden of evaluating multigroup neutron diffusion eigenvalue problems. PGD is a reduced order modeling technique that seeks a separated representation to a multi-dimensional variable. In this application, each multigroup flux is sought as a finite sum of separable one-dimensional functions. This representation can significantly reduce the burden of evaluating multi-dimensional linear systems. Therefore, we use PGD to evaluate the linear systems within the power iteration process of the eigenvalue problem. In this paper, we discuss our implementation of PGD to these eigenvalue systems including a derivation of PGD operators for multigroup neutron diffusion problems with standard power iteration and power iteration accelerated with adaptive Wielandt shift. To illustrate PGD’s effectiveness, we apply our implementation to eigenvalue problems ranging from homogeneous to highly heterogeneous geometries with one-,two-, and four-group material properties. With comparison to full-order model evaluation with MOOSE, we find that the effectiveness of PGD is problem dependent. PGD always out performs the full-order model with close to homogeneous problems, but performs more poorly with more realistic reactor problems.

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Research Organization:: Texas A & M Univ., College Station, TX (United States). Texas A & M Engineering Experiment Station

Sponsoring Organization:: USDOE; USDOE Office of Nuclear Energy (NE)

Grant/Contract Number:: NE0000112

OSTI ID:: 1801174

Journal Information:: Progress in Nuclear Energy, Journal Name: Progress in Nuclear Energy Journal Issue: C Vol. 121; ISSN 0149-1970

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Application of proper generalized decomposition to multigroup neutron diffusion eigenvalue calculations

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