On the Fundamental and Higher-Mode Eigenpairs of Fission Matrix Method and p-CMFD Method in Continuous-Energy Monte Carlo Calculation

In a similar work, coarse-mesh finite difference (CMFD) acceleration of multi-group MC calculation was proposed by Lee et al.. In this exploratory paper, any relationship between fission matrix and p-CMFD matrices is investigated by applying them to a 1-D continuous-energy thermal reactor test problem. The fundamental and higher-mode eigenpairs are calculated and compared. The structure, fundamental and higher-mode eigenpairs of the fission matrix obtained from the fission matrix method and the p-CMFD method, respectively, are compared using the numerical results on a test problem reactor with reflector region. The fission matrix method gives eigenmodes in fission source distributions, but not in flux distributions. Thus, flux distribution in the non-fissile region of the reactor is not available. However, the p-CMFD method gives eigenmodes in both variables. The numerical results indicate that the fundamental-mode eigenpairs from the two methods are practically identical, but the higher-mode eigenpairs exhibit some differences. The dominance ratio in the p-CMFD method is smaller than that in the fission matrix method, if the coarse-mesh is not too fine. This implies that the p-CMFD method converges faster than the fission matrix method if it is used as low-order equation in acceleration of Monte Carlo calculation. It is also noted that the storage required is linear in N (=number of cells) in the p-CMFD method, while it is quadratic in the fission matrix method