Convergence analysis of the non-linear CMFD schemes for acceleration of multi-group fixed source neutron transport calculations

Abstract

The coarse mesh finite difference (CMFD) and related methods have been some of the most extensively used schemes to accelerate the convergence of neutron transport iterations. Despite its predominant application on multi-group problems, the convergence behavior of this class of acceleration methods has been traditionally characterized for the one-group form and results extended to multi-group domain. Theoretical convergence analysis of the multi-group variants of CMFD scheme has not been previously performed and is an important work related to neutron transport studies. Fourier analysis of the coarse mesh finite difference (CMFD), partial current CMFD (pCMFD) and optimally diffusive CMFD (odCMFD) methods for acceleration of the multi-group fixed source neutron transport calculations has been presented in this paper. The multi-group error transition matrix and intermediate Fourier analysis expressions have been found to be analogous to those for one-group system. Sensitivity studies to characterize the effect of various parameters on the overall convergence behavior have also been presented. The results extend current understanding and provide deeper insight into the application of CMFD class of acceleration schemes for more realistic multi-group calculations.