Operator-level relationship between classical variational and nonclassical asymptotic SPN formulations
Sunday A. Agbo, Leonardo R. C. Moraes, Richard Vasques · Annals of Nuclear Energy · 2026
The relationship between classical variational SP N /GSP N formulations and asymptotic nonclassical SP N formulations is examined at the level of the governing reduced operators. In particular, the classical variational SP N operator is compared with the asymptotic SP N hierarchy obtained from the nonclassical spherical harmonics approximation (NSHA) applied to the nonclassical transport equation. It is shown that the SP N equations obtained from the classical variational formulation of Mishra et al. are recovered as the exponential free-path specialization of the NSHA-derived asymptotic operator hierarchy. In this limit, the moment-dependent nonclassical transport coefficients reduce to their classical forms and the NSHA-derived equations recover the classical SP N system exactly. When the free-path distribution departs from exponential form, the asymptotic NSHA formulation yields modified transport coefficients that cannot be recovered within the classical variational coefficient set. This operator-level comparison identifies the free-path moment conditions under which the classical variational formulation is recovered and clarifies how non-exponential free-path statistics modify the reduced SP N coefficient structure. Controlled numerical benchmarks compare classical and nonclassical SP N solutions for prescribed non-exponential free-path statistics. The calculations confirm coincidence in the exponential limit and demonstrate systematic coefficient-driven separation when the free-path moments depart from the classical exponential sequence. A deterministic GLBE reference-solution comparison is also included for the SP 1 coefficient correction, illustrating the role of moment-informed coefficients in nonclassical reduced transport models. These results clarify the scope of the classical variational SP N formulation and provide a basis for selecting moment-informed SP N coefficients in deterministic transport calculations involving non-exponential free-path statistics.