Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

• 作者: Dan Gabriel Cacuci Ruixian Fang
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Polyethylene-Reflected Plutonium Sphere 1^st-Order 2^nd-Order and 3^rd-Order Sensitivities 3^rd-Order Adjoint Sensitivity Analysis Microscopic Total Cross Sections Expected Value Variance and Skewness of Response Distribution
• 年，卷（期）: 2020,（4）
• 页码范围: 503-528
• 页数: 26页
• 分类号: O17

摘要

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)² second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1^st- and 2^nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)³ third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3^rd-order sensitivities of the leakage 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 these (180)³ third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.