• 에너지공학
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• 제17권4호
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• pp.233-240
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• 2008

최근 새로운 2계 자기 수반형(self-adjoint) 중성자 수송 방정식으로 기존의 우성 및 기성 수송 방정식 외에 SAAF(Self-Adjoint Angular Flux) 수송 방정식이 소개되어, 이에 대한 적절한 경계조건, 수치해법, 정확도 등에 관한 논의가 활발히 진행되고 있다. 본 연구에서는 SAAF 수송 방정식의 수학적, 물리적 의미를 고찰하고 기존의 우성 및 기성 수송 방정식과의 연관성을 명확히 하였으며, Boltzmann 수송 방정식의 1계 차분식에서 2계의 SAAF 수송 방정식의 차분식을 유도하는 방법을 확산 가속법(diffusion synthetic acceleration method)과 함께 소개하였다. 유도된 SAAF 차분법이 계산 효율성과 수송해의 정확도를 증가시킴을 수치결과로 확인하였다.

• Nuclear Engineering and Technology
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• 제56권11호
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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.