A new moving-mesh Finite Volume Method for the efficient solution of two-dimensional neutron diffusion equation using gradient variations of reactor power

Vagheian, Mehran; Ochbelagh, Dariush Rezaei; Gharib, Morteza

doi:10.1016/j.net.2019.02.011

Cited by 3 publications

(1 citation statement)

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“…In this context, although the theory of neutron diffusion for global calculations in reactor physics has limited validity, it is widely used because it provides satisfactory results for many applications. One of them is the analysis of the criticality of nuclear reactors [1,3,7,15], where the main issue is to establish the ratio between the numbers of neutrons generated in successive fission reactions. In this way, the criticality is evaluated by the dominant eigenvalue of the stationary Neutron Diffusion Equation and its corresponding eigenvector is associated with the neutron scalar flux.…”

Section: Introductionmentioning

confidence: 99%

A Nodal-iterative Technique for Criticality Calculations in Multigroup Neutron Diffusion Models

Zanette

Barichello

Petersen

2022

TCAM

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In this work, a nodal and iterative technique to evaluate the effective multiplication factor as well as the neutron flux, in multigroup diffusion problems, is presented. An iterative scheme, similar to the source iteration method, is implemented to decouple the system of differential equations which is the fundamental mathematical model. Then, analytical solutions are derived for the one-dimensional transverse integrated equations, of each energy group, resulting from a nodal approach. Constant approximations are assumed for the unknown transverse leakage terms in the contours of the nodes. In addition, constant and linear representations are investigated to express the fluxes in the source term to be updated in the iterative process. Numerical results for the effective multiplication factor were obtained for a series of two-dimensional multigroup problems with up-scattering and down-scattering. The procedure is simple, fast, the analysis of the results indicated a satisfactory agreement with results available in the literature and the use of different approximations to the source term seems to be a good alternative, instead of using higher-order approximations on the contour of the nodes, to improve accuracy.

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Section: Introductionmentioning

confidence: 99%