A modified power method for the multilayer multigroup two-dimensional neutron diffusion equation

Zanette, Rodrigo; Petersen, Claudio Zen; Schramm, Marcelo; Zabadal, Jorge Rodolfo Silva

doi:10.1016/j.anucene.2017.08.059

Cited by 2 publications

(9 citation statements)

References 6 publications

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“…We solved four test problems, to which results are available in the literature [6,9,13,18], for the sake of comparisons. In our calculations, the fluxes in the source term are updated by constant and linear approximations, in order to analyze the influence of the approximation orders.…”

Section: Resultsmentioning

confidence: 99%

“…This first problem we consider is a two groups heterogeneous medium problem proposed in Ref. [18]. The geometry is defined as a rectangular domain, [0, 36] × [0, 12] (cm), divided into three 12 cm × 12 cm regions (see Fig.…”

Section: Problemmentioning

confidence: 99%

“…Zero flux is assumed as boundary conditions for all boundaries. (2.1), we follow [18] and the cross sections for each group are given in Table 1.…”

Section: Problemmentioning

confidence: 99%

“…In 2018, [18] proposed a methodology to solve the multigroup multilayer stationary neutron diffusion equation in two-dimensional Cartesian geometry through the source iteration method. The Fourier Transform was used to develop an analytical solution in each step of the source iteration, instead of using traditional numerical methods.…”

Section: Introductionmentioning

confidence: 99%

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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: Resultsmentioning

confidence: 99%

Section: Problemmentioning

confidence: 99%

“…Zero flux is assumed as boundary conditions for all boundaries. (2.1), we follow [18] and the cross sections for each group are given in Table 1.…”

Section: Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Zanette

Barichello

Petersen

2022

TCAM

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“…The power iteration (PI) method is the most used method to obtain the fundamental eigenvalue and its eigenvector [18]. This iterative source method is described in detail by [19]. The power iteration algorithm process is as follows.…”

Section: Power Iterationmentioning

confidence: 99%

Richardson Extrapolation‐Based Verification Method of Scientific Calculation Program without the Oracles: A Case Study

Yan

Yang

Cheng

et al. 2019

Mathematical Problems in Engineering

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For the verification test of some scientific calculation programs, different comparison methods are commonly applied to ensure the correctness of the computations. However, it is difficult to verify whether the testing output is correct, because the oracles which include the expected output are not always available or too hard to get. For this reason, the authors focus on using the Richardson Extrapolation to estimate the convergences of the numerical solution on different levels of mesh refinement. These numerical convergence properties can be applied to verification test, without the need for giving the oracles. In the present study, the authors take the program test of the multigroup neutron diffusion equations as a study case and propose the Richardson Extrapolation-based verification method. Three verification criterions are obtained based on our approach. In addition, a test experiment is conducted demonstrating the validity of our theoretical results.

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A modified power method for the multilayer multigroup two-dimensional neutron diffusion equation

Cited by 2 publications

References 6 publications

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

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

Richardson Extrapolation‐Based Verification Method of Scientific Calculation Program without the Oracles: A Case Study

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