Iterative acceleration methods for Monte Carlo and deterministic criticality calculations.

Abstract

Criticality calculations use the source iteration method and serve an increasingly prominent role in the nuclear community. Of late, the more important calculations are not only for reactors, but for nuclear waste storage configurations. Unfortunately, these types of systems have large dominance ratios and pose the largest computational difficulty for both Monte Carlo and deterministic methods. Typical systems with high dominance ratios are arrays of barrels of nuclear waste and large thermal reactors. These systems often require enormous computing times to converge the fission source. We have developed three new methods that remedy these slow-converging problems. The first two methods are acceleration methods. Each accelerated iteration has an additional step where a low-order approximation to an exact correction is applied to the fission source. The extra work at each iteration is more than compensated by the accelerated convergence. The Fission Matrix Acceleration method uses the fission matrix as a low-order operator in an acceleration equation that speeds fission source convergence. The Fission Diffusion Synthetic Acceleration method is similar, but instead uses the low-order diffusion approximation. These two acceleration methods converge to the same solution as the unaccelerated methods, only faster. The Monte Carlo acceleration methods require the selection of two parameters for damping and filtering the statistical noise. Unfortunately, this selection is not automated. Sometimes, for difficult problems, the Monte Carlo method does not converge to the correct solution, so these acceleration methods do not converge either. For these problems, a Hybrid Monte Carlo method overcomes inherent Monte Carlo deficiencies, converges the fission source, and displays a much-reduced variance. These methods were tested on simple, idealistic problems that contain enough realistic properties to demonstrate the feasibility of the methods and study their behavior. For these problems, computer time speedups were 5-10 for Monte Carlo acceleration, up to nearly two orders of magnitude for deterministic acceleration, and arbitrarily large for the Hybrid Monte Carlo method. Also, the Fission Matrix Acceleration method was successfully implemented in the production Monte Carlo code MCNP$\sp{\rm TM}$ for a three-dimensional, continuous-energy problem, demonstrating a speedup of more than 5.