Fourier convergence analysis of two-node coarse-mesh finite difference method for two-group neutron diffusion eigenvalue problem

Abstract

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problem. The explicit expression of current correction factor (CCF) has been derived based on the analytic two-node nodal method (ANM2N) and Fourier analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by Fourier analysis compares very well with the numerically measured convergence rate. It is also noted that the convergence rate of CCF of CMFD2N algorithm is dependent on the mesh size but not on the total problem size, which is contrary to the expectation for eigenvalue problem. To the best knowledge of authors, the analytical derivation of the convergence rate of CMFD2N algorithm for the eigenvalue problem has never been published anywhere before.