Acceleration and Stabilization Methods for Monte Carlo Reactor Core k-Eigenvalue Problems.

Abstract

Typical Monte Carlo (MC) reactor core k-eigenvalue simulations are large and complex, requiring many inactive cycles to converge the fission source. In a 2009 publication, a hybrid MC method was proposed in which the fission source convergence is “accelerated” at the end of each inactive MC cycle using the solution of a discrete low-order Coarse Mesh Finite-Difference (CMFD) equation. This method has been implemented in several codes, but is sometimes unstable. In this work, we extend existing research on this CMFD-MC method and its variants. To delve deeper into the numerical stability issue, we perform a Fourier analysis on the “non-random” CMFD-MC iteration scheme (which assumes an infinite number of particles per cycle). Spectral radius results indicate that the CMFD-MC method becomes unstable for certain coarse-grid/ scattering ratio combinations, even in the infinite-particle limit. We also investigate a new MC iteration strategy, in which particles are allowed to undergo a fixed maximum number of collisions per cycle. We call this the Limited-Collision Monte Carlo (LCMC) method. This particular strategy was chosen to significantly shorten the computation time per MC cycle; however, a Fourier analysis predicts (and numerical results support) that this iteration is less stable than CMFD-MC for a given coarse grid size when the number of permitted collisions per cycle is small. This observation led us to design and implement a new simulation procedure, which makes use of both the CMFD-MC and LCMC iterations. Our iteration scheme employs standard CMFD-MC during inactive cycles to efficiently converge the fission source, then transitions to the modified Limited-Collision Monte Carlo (LCMC) algorithm to improve the efficiency of active cycles. By implementing this procedure, we show that it is possible to solve reactor core k-eigenvalue problems using two different MC algorithms. We refer to this simulation strategy as the “mixed” method (indicating a hybrid simulation, employing both the CMFD-MC and LCMC iteration schemes). Results for a large 1-D problem indicate a factor of 3-5 improvement in the solution Figure of Merit (FOM) over the current “state of the art” method.