Solution of the neutron diffusion equation in hexagonal geometries |
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| Affiliation: | 1. Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, USA;2. Advanced Research Group, Korea Atomic Energy Research Institute, 70 Daedeok-daero 989 Beon-gil, Yuseong-gu, Daejeon 34057, Republic of Korea;3. NSSS Design Group, Korea Hydro & Nuclear Power Co., Ltd., Central Research Institute, 70, 1312-beongil, Yuseongdaero, Yuseong-gu, Daejeon, Republic of Korea;1. Department of Nuclear Engineering and Technology, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China;1. Politecnico di Torino, Dipartimento Energia, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy;2. I.N.F.N., Sezione di Torino, Via P. Giuria, 1, 10125 Torino, Italy;3. I.N.F.N., Sezione di Genova, Via Dodecaneso, 33, 16146 Genova, Italy |
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| Abstract: | Various ways to solve the neutron diffusion equation in hexagonal geometries are known in the literature. In this paper it is aimed to unify these approaches from different points of view. First conditions are developed for consistency and uniqueness of the various approximations; they are then used to derive estimates of the order of the corresponding rates of convergence. Then several approximations are formulated explicitly and related to the theoretical considerations, and their mutual dependencies are shown. Finally, numerical experiments are reported which support the theoretical findings. |
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