Fourth-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: II. Mathematical Expressions and CPU-Time Comparisons for Computing 4<sup>th</sup>-Order Sensitivities
- 1 Center for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA
- 2 Center for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA
Abstract
This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a p oly e thylene- r eflected p lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. Previous works showed that the third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections are far larger than the corresponding 1 st -order and 2 nd -order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4 th -order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4 th -order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross sections, and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.
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