Convergence study of variants of CMFD acceleration schemes for fixed source neutron transport problems in 2D Cartesian geometry with Fourier analysis

Abstract

Abstract Previous works have derived the Fourier analysis for different CMFD based neutron transport acceleration schemes for 1D problems to study the convergence performance, in which the recently developed lpCMFD scheme gives best convergence performance due to its employment of linear prolongation technique in flux updating that maintains continuous flux at the coarse mesh boundary. However, the theoretical convergence performance for variants of CMFD schemes in 2D neutron transport problems has not been previously investigated and is an important result that will complement other studies of neutron transport acceleration methods. This paper carries out the Fourier analysis of the CMFD, pCMFD, odCMFD and lpCMFD acceleration schemes for the fixed source neutron transport problem in two dimension, along with detailed linearization and formulation derivation. The Fourier analysis results show that compared to other schemes, the lpCMFD scheme has the lowest spectral radius for coarse mesh optical thickness larger than 1 and is unconditionally stable for scattering ratios c\u202f=\u202f0.6, 0.8, 0.9 and 0.99 for a large range of coarse mesh optical thicknesses up to 100, which are consistent with 1D findings. It is also shown that there is almost no impact of the choice of level-symmetric SN quadrature set on the spectral radius. The results presented here can support the application of lpCMFD for fixed source neutron transport problems in 2D space for practical problems. Our research provides valuable insight to the field of acceleration methods in neutron transport.