Convergence analysis of coarse mesh finite difference method applied to two-group three-dimensional neutron diffusion problem

Abstract

This article presents the convergence analysis of the coarse mesh finite difference (CMFD) method applied to two-group (2-G) three-dimensional (3D) neutron diffusion problem. Two CMFD algorithms are examined: one-node (1-N) CMFD and two-node (2-N) CMFD. Two test problems are used for the study of the convergence behavior: a model problem of homogeneous 2-G 3D eigenvalue problem and the NEACRP LWR transient benchmark problem. The convergence rates of the 1-N and 2-N CMFD algorithms are numerically measured in terms of the convergence of current correction factors (CCFs). The numerical test results are presented as well as the comparison with the previous analytical study. Overall, 1-N CMFD with the CCF relaxation shows a comparable performance to 2-N CMFD for the realistic 3D rod ejection transients.

The Source Equivalence Acceleration Method

“…[1] If CMFD is able to converge for an optically thick problem, little to no acceleration is observed. [12] In many applications of CMFD, a dampening factor is applied to prevent instabilities from growing and causing divergence. The dampening factor prevents overshoot of the accelerated scalar fluxes by limiting how quickly the nonlinear diffusion coefficient correction factor from Equation (2.1) is updated.…”