Impact of Dynamic Condensation of Energy Groups on Convergence Behavior of One-Node CMFD Method for Neutron Diffusion Problem

The impact of the dynamic condensation of energy groups on the convergence characteristics of the coarse mesh finite difference (CMFD) algorithm has been analyzed within the framework of two-group (2-G) one-node (1-N) local kernel (CMFD1N) and one-group or 2-G global CMFD formulations. Three algorithms were analyzed by the method of linearizing the nonlinear algorithms and applying Fourier analysis to the linearized algorithms: partial current sweep (PCS), CMFD1N, and CMFD1N with dynamic condensation (CMFD1N-DC). Because of the dynamic condensation, the spectral radius of the CMFD1N-DC algorithm is influenced by the other two algorithms; i.e., it shows a similar behavior to the PCS algorithm for small mesh sizes and a similar behavior to the CMFD1N algorithm for large mesh sizes. From the theoretical derivation, it was shown that the spectral radius is determined by the combination of partial current spectrum update in the local PCS kernel and the current correction factor update in the global CMFD. Specifically, the convergence properties of the CMFD1N-DC algorithm follow those of the PCS algorithm for small mesh sizes since the energy spectrum is only updated in the local kernel. It was also observed that the relaxation parameter for the CMFD1N-DC algorithm needs to be determined with the fast group cross-section data because of the dynamic condensation.