A Fission Matrix Based Methodology for Achieving an Unbiased Solution for Eigenvalue Monte Carlo Simulations

Abstract

*Recent work in the completely fission matrix based Monte Carlo eigenvalue methodology has posited that the fission matrix elements are independent of the source eigenvector in the limit of small mesh sizes. In this paper, a modified fission matrix based Monte Carlo methodology for achieving unbiased solutions even for high Dominance Ratio (DR) problems is introduced. This new methodology utilizes an initial source, autocorrelation and normality tests, in addition to a Monte Carlo Iterated Confidence Interval (ICI) formulation for estimation of uncertainties in the fundamental eigenvalue and eigenvector. This new methodology is referred to as FMBMC-ICEU (Initial-source Controlled Elements with Uncertainties). The mesh size and particle population were shown to be directly related to the independence of fission matrix coefficients whereby smaller meshing with increasing particle density is necessary to achieve an unbiased solution for the high Dominance Ratio problems. Additionally, it is shown that the ICI algorithm yields a more realistic estimation of uncertainties as compared to the highly conservative plus or minus fission matrix based approach. Lastly the parallel capability of the algorithm was tested and shown to be highly scalable if the number of skipped generations is minimized.