A variational nodal formulation for multi-dimensional unstructured neutron diffusion problems

Sun Qizheng; Xiao Wei; Li Xiangyue; Yin Han; Zhang Tengfei; Liu Xiaojing

doi:10.1016/j.net.2023.02.021

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자료유형: 학술저널

저자정보: Sun Qizheng (Shanghai Jiao Tong University) Xiao Wei (Shanghai Jiao Tong University) Li Xiangyue (Shanghai Jiao Tong University) Yin Han (Shanghai Jiao Tong University) Zhang Tengfei (Shanghai Jiao Tong University) Liu Xiaojing (Shanghai Jiao Tong University)

저널정보: 한국원자력학회 Nuclear Engineering and Technology Nuclear Engineering and Technology 제55권 제6호

발행연도: 2023.6

수록면: 2,172 - 2,194 (23page)

DOI: 10.1016/j.net.2023.02.021

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A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are pro posed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (keff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2e3

#Variational nodal method #Unstructured mesh #Neutron diffusion equation #Neutron dynamic equation #Partitioned matrix acceleration

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