On the convergence of the rebalance methods for transport equation for eigenvalue problems

This paper analyzes the convergence of the rebalance iteration methods (e.g., Coarse-Mesh Rebalance (CMR), Coarse-Mesh Finite Difference (CMFD), and Partial Current-Based Coarse Mesh Finite Difference (p-CMFD) for accelerating the power iteration method of the discrete ordinates transport equation in the eigenvalue problem. The convergence analysis is performed with the well-known Fourier analysis through a linearization both for the spatially continuous and discretized forms of one and two energy group transport equations in an infinite medium. The analysis assumes that one outer iteration consists of one transport sweeping for each energy group and an update of the eigenvalue, fission source, and the scattering sources. This paper presents the formulations of the analyses and their results. The results show that the convergences of the rebalance methods and the original power iteration method for the eigenvalue problem can be analyzed with the methods for the fixed source problem after transforming the scattering cross sections into a different set of cross section, and that this analysis provides a fairly good estimation of the spectral radius of the power iteration of the discrete ordinate transport equation.