A Functional Monte Carlo Method for k-Eigenvalue Problems.

摘要

A longstanding problem for Monte Carlo (MC) criticality simulation is the slow convergence of the fission source distribution for systems with a high dominance ratio (DR). In this thesis, we have developed and tested a new hybrid deterministic and MC method, called the Functional Monte Carlo (FMC) method, to solve such problems. We show herein that the FMC method produces a significant improvement in the speed of convergence and accuracy of criticality calculations, which are particularly important for nuclear reactor operation and design, as well as for nuclear safety applications. Different from any previous hybrid method, the FMC method does not directly estimate the eigenfunction and eigenvalue via MC particle simulation. Instead, it uses MC techniques to directly estimate certain nonlinear functionals. These functionals are then used in the low-order FMC equations to calculate the k-eigenfunction and eigenvalue. The resulting estimates have no spatial or angular truncation errors, and are generally more accurate than estimates obtained using conventional MC methods.;The FMC method is based on two assumptions: (1) The functionals depend weakly on the angular flux and can be evaluated with MC more accurately than direct MC estimates of the angular or scalar flux. (2) If the low-order FMC equations are solved with small errors in the functionals, the resulting errors in the eigenfunction and eigenvalue will be small.;In this work, we have developed the FMC method for monoenergetic, multigroup, and continuous energy k-eigenvalue problems in 1-D planar geometry. We have tested the FMC method on various problems, in which standard MC estimates of the eigenfunction tend to "wobble." Our numerical results indicate that the fission source distribution is found to converge orders of magnitude faster using the FMC approach. Inter-cycle correlation is very weak for the FMC method. The true and apparent relative errors are about the same for the FMC method. And with FMC feedback, the performance of MC estimates of the eigenfunction improved significantly. For future research, it remains to extend the FMC method to include realistic cross sections and multi-dimensional problems. We see no fundamental impediment to doing this.