• Journal of Energy Engineering
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• v.17 no.4
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• pp.233-240
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• 2008

Conventionally, the second-order self-adjoint neutron transport equations have been studied using the even parity and the odd parity equations. Recently, however, the SAAF(self-adjoint angular flux) form of neutron transport equation has been introduced as a new option for the second-order self-adjoint equations. In this paper we validated the SAAF equation mathematically and clarified how it relates with the existing even and odd parity equations. We also developed a second-order SAAF differencing formula including DSA(diffusion synthetic acceleration) from the first-order difference equations. Numerical result is attached to show that the proposed methods increases accuracy with effective computational effort.

• Nuclear Engineering and Technology
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• v.56 no.11
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• pp.4551-4562
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• 2024

This paper elucidates a comprehensive derivation of the variational formulation pertaining to the static and spatial kinetics self-adjoint angular flux (SAAF) neutron transport equation. The methodology employed for discretization of the spatial variable is the finite element method, while the energy group discretization is executed via the group method, and the directional discretization is conducted using the discrete ordinates method. Analytic expressions for the discretization to variable separation under both vacuum and reflective boundary conditions are furnished. Constructed upon the MOOSE framework, a code designated as SAAFCGSN has been developed for the resolution of the SAAF neutron transport equation. The zero-order scattering matrix within this computational framework is managed through an innovative "decoupling" method, thereby enhancing the computational efficiency significantly. The functionality and robustness of the SAAFCGSN code are corroborated through meticulous evaluation involving seven distinct steady-state scenarios as well as two transient states. Empirical outcomes verify the compatibility of the SAAFCGSN code with both structured and unstructured mesh, inclusive of their amalgamations, thus facilitating maintenance and ensuring elevated computational accuracy. In addition, a performance analysis benchmarked against IAEA standards reveals that the adoption of the scattering matrix "decoupling" method propels a computational speed increase exceeding 30 %, signifying a notable advancement in calculation efficiency.