Stability analysis of CMFD acceleration for the wavelet expansion method of neutron transport equation

This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is...

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Bibliographic Details
Published in:Nuclear engineering and design 2013-01, Vol.254, p.142-147
Main Authors: Zheng, Youqi, Wu, Hongchun, Cao, Liangzhi
Format: Article
Language:English
Subjects:
Acceleration
Applied sciences
Controled nuclear fusion plants
Eigenvalues
Energy
Energy. Thermal use of fuels
Exact sciences and technology
Fission nuclear power plants
Fourier analysis
Fuels
Installations for energy generation and conversion: thermal and electrical energy
Nuclear fuels
Scattering
Spectra
Stability
Stability analysis
Wavelet
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Summary:This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is defined as the stability criterion, which is the least upper bound (LUB) of the largest eigenvalue of Fourier analysis matrix. The stability analysis considers the effect of mesh size (spectral length), coarse mesh division and scattering ratio. The results show that for the wavelet expansion method, the CMFD acceleration is conditionally stable. The small size of fine mesh brings stability and fast convergent. With the increase of the mesh size, the stability becomes worse. The scattering ratio does not impact the stability obviously. It makes the CMFD acceleration highly efficient in the strong scattering case. The results of Fourier analysis are verified by the numerical tests based on a homogeneous slab problem.
ISSN:0029-5493
1872-759X
DOI:10.1016/j.nucengdes.2012.09.016