Fourth-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: II. Mathematical Expressions and CPU-Time Comparisons for Computing 4&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt;-Order Sensitivities

Dan Gabriel Cacuci,Ruixian Fang

doi:10.4236/ajcm.2021.112010

Abstract

This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (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 1st-order and 2nd-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 4th-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4th-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.

Highlights

IntroductionThis work is organized as follows: Section 2 presents the methodology for deriving the analytical expressions of the exact 4th-order sensitivities of the PERP benchmark’s leakage response with respect to the total microscopic cross sections
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 1st-order and 2nd-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response
Dology (4th-CASAM) for linear system [1], this work extends the results reported in the accompanying Part I [2] by presenting the derivation of the expressions of the 4th-order sensitivities of the leakage response of the polyethylene-reflected plutonium OECD/NEA reactor physics benchmark [3] to the PERP benchmark’s 180 group-averaged total microscopic cross sections

Summary

Introduction

This work is organized as follows: Section 2 presents the methodology for deriving the analytical expressions of the exact 4th-order sensitivities of the PERP benchmark’s leakage response with respect to the total microscopic cross sections. This section continuing the work presented in Part I [2] presents the derivation of the exact analytical expressions of the 4th-order sensitivities of the leakage response of the polyethylene-reflected plutonium (acronym: PERP) metal sphere OECD/NEA benchmark [3] with respect to this benchmark’s total microscopic cross sections. The 4th-CASAM will be discussed in Subsection 2.2.3, while Subsection 2.2.4 will present a comparative discussion of the computational resources and times (CPU) which are required by these three deterministic methods

Re-Computations with Finite-Difference Approximation

Concluding Remarks