Numerical stability analysis of lp-CMFD acceleration for the discrete ordinates neutron transport calculation discretized with discontinuous Galerkin Finite Element Method

Chan, Yimeng; Xiao, Sicong

doi:10.1016/j.anucene.2020.108036

Annals of Nuclear Energy

2021

DOI: 10.1016/j.anucene.2020.108036

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Numerical stability analysis of lp-CMFD acceleration for the discrete ordinates neutron transport calculation discretized with discontinuous Galerkin Finite Element Method

Yimeng Chan

Sicong Xiao

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A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

Zheng

et al. 2022

Front. Energy Res.

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Coarse-mesh finite difference (CMFD) method is a widely used numerical acceleration method. However, the stability of CMFD method is not good for the problems with optically thick regions. In this paper, a stability rule named the “sign preservation rule” in the field of numerical heat transfer is extended to the scheme of CMFD. It is required that the disturbance of neutron current is positively correlated with that of the negative value of flux gradient. A necessary condition for stability of the CMFD method is derived, an adaptive diffusion coefficient equation is proposed to improve the stability of CMFD method, and the corresponding revised CMFD method is called the rCMFD method. With a few modifications of the code, the rCMFD method was implemented in the hexagonal-Z nodal SN (discrete-ordinates) solver in the NECP-SARAX code system. The rCMFD method and other similar acceleration methods were tested by three fast reactor problems which were obtained by modifying the hexagonal pitches of a benchmark problem. The numerical results indicated that the rCMFD method showed better stability than the traditional CMFD method and the artificially diffusive CMFD (adCMFD) method and a better convergence rate than the adCMFD method and the optimally diffusive CMFD (odCMFD) method for these fast reactor problems.

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A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

Zheng

et al. 2022

Front. Energy Res.

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show abstract

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Numerical stability analysis of lp-CMFD acceleration for the discrete ordinates neutron transport calculation discretized with discontinuous Galerkin Finite Element Method

Cited by 1 publication

References 18 publications

A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

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