Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

Journal Article · 10 February 2019 · Nuclear Science and Engineering

DOI: https://doi.org/10.1080/00295639.2018.1565014 · OSTI ID:1514983

McClarren, Ryan Gerard  ^[1]

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1. Univ. of Notre Dame, Notre Dame, IN (United States)

A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time-dependent transport equation. Using these solutions, we use the dynamic mode decomposition to form an approximate transport operator. This approximate operator has eigenvalues that are mathematically related to the time eigenvalues of the neutron transport equation. This approach works for systems of any level of criticality and does not require the user to have estimates for the eigenvalues. Numerical results are presented for homogeneous and heterogeneous media. The numerical results indicate that the method finds the eigenvalues that contribute the most to the change in the solution over a given time range, and the eigenvalue with the largest real part is not necessarily important to the system evolution at short and intermediate times.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1514983
• Report Number(s): LA-UR--18-30110
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 8 Vol. 193; ISSN 0029-5639
• Publisher: American Nuclear Society - Taylor & FrancisCopyright Statement
• Country of Publication: United States
• Language: English