Convergence Analysis of Two-Node CMFD Method for Two-Group Neutron Diffusion Eigenvalue Problem

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. There have been several successes applying the Cefus and Larsen's approach to algorithms with fixed source neutron diffusion problems. It is numerically and analytically proven that the convergence rate for CMFD2N algorithm is independent of the whole problem size but dependent on only the mesh size, and also unconditionally stable at least for the given problem. The convergence rate of the CMFD2N algorithm is explicitly calculated by Fourier analysis. From the form of the analytically calculated convergence rate, it is possible to know that the convergence rate is dependent on a product of the mesh size and the converged second harmonic buckling, which is defined by cross section data. The theoretically calculated convergence rate is identical with the numerically measured convergence rate. It is analytically proven that the convergence rate is unconditionally stable for the neutron diffusion eigenvalue problem