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

•Fourier analysis of CMFD based acceleration schemes for multi-group fixed-source neutron transport calculations is performed.•Linearization of the non-linear CMFD techniques and detailed derivation of multi-group error iteration matrix is presented.•Fourier analysis formulation of the multi-group CMFD methods is shown to be block analogous to existing one-group results.•Effect of various parameters on convergence performance of multi-group CMFD, pCMFD and odCMFD schemes is investigated.•pCMFD and odCMFD are unconditionally stable for all coarse mesh sizes even with large scattering ratios in multiple groups.