Convergence study of CMFD based acceleration schemes for multi-group transport calculations with fission source using fourier analysis

• Published in: Annals of nuclear energy 2021-09, Vol.160, p.108314, Article 108314
• Main Authors: Jain, Lakshay, Mohanakrishnan, Prabhakaran, Karthikeyan, Ramamoorthy, Kannan, Umasankari
• Format: Article
• Language: English
• Subjects: Acceleration schemes; Coarse mesh finite difference (CMFD); Convergence; Fission source; Fourier analysis; k-eigenvalue problem; Multigroup; Neutron transport
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2021.108314

•Fourier analysis of CMFD accelerated multigroup criticality calculations performed.•Linearization of CMFD schemes presented and multigroup error iteration matrix derived.•Multigroup Fourier analysis formulation shown to be block analogous to one-group case.•Effect of various parameters on spectral radii of multigroup CMFD schemes investigated.•CMFD diverges for optically thick coarse cells; pCMFD/odCMFD are unconditionally stable. Application of the coarse mesh finite difference (CMFD) method and its variants to accelerate the convergence of criticality calculations has been extremely popular for neutron transport simulations. Despite their widespread use in the multi-group form, the convergence performance of these acceleration schemes is usually studied in the one-group domain and results extended to multi-group problems. Theoretical investigation of the convergence behavior of multi-group CMFD and related methods has not been previously performed and is an important work to complement existing studies. In this paper, we present the Fourier convergence analysis of multi-group CMFD, partial current CMFD (pCMFD), optimally diffusive CMFD (odCMFD) and linear prolongation CMFD (lpCMFD) schemes for acceleration of the fission source neutron transport calculations. The multi-group formulation of the error iteration matrix has been found to be analogous to the results obtained from one-group analysis. It has also been shown that for certain simplified cases, the spectral radius of multi-group CMFD is independent of the group coupling terms and can be determined as the maximum among individual energy groups. The results extend current understanding and provide deeper insight into the application of CMFD based acceleration techniques for more realistic multi-group neutron transport.