A fission collision separation method for efficient incident flux response expansion coefficient generation

Abstract

A new fission collision (generation) separation method has been developed for generating incident flux response expansion coefficients and implemented into the hybrid stochastic/deterministic coarse mesh transport (COMET) method for whole core criticality (eigenvalue) calculations. During the stochastic pre-computation of the response library, all coefficients associated with each fission neutron generation are tallied separately. This enables COMET to directly calculate the eigenvalue (k) dependent response coefficients on-the-fly as a superposition of contributions from the nth fission neutron generation scaled by the factor 1kn. The new method is as accurate as or more accurate and significantly more efficient than the existing response methods, regardless of whether the fission source is treated explicitly or implicitly as in COMET. The method also removes the eigenvalue range restriction on the response library.The 3D C5G7 benchmark problem was used to test the accuracy and efficiency of the new response coefficient generation method at both lattice (local) and core (global) levels. For lattice calculations, the response coefficients computed by the new method were compared with those computed by the direct Monte Carlo method. It was found that the truncation errors of the fission neutron separation method at expansion order 3 are much lower than the stochastic uncertainties of the response coefficients and consequently can be ignored. The average truncation errors of the new method ranged from 0% to 0.004% and 0% to 0.08% for the surface-to-surface and fission density response coefficients, respectively. For core level calculations, the COMET whole-core solutions based on the response coefficient libraries generated by the new method and the interpolation method were compared with direct (reference) Monte Carlo calculations using the MCNP code. It was found that the error in the eigenvalues predicted by COMET based on the new method is within 11–26pcm for three core configurations with and without control rods. These eigenvalue results are about 15pcm more accurate than those based on the interpolation method, although still within the overall uncertainty. The corresponding assembly and pin fission densities are almost identical for the two methods. These comparisons indicate that the new method is as accurate as or slightly more accurate than the interpolation method, depending on the comparison parameter. The new method was found to be about 5 times faster than the interpolation method for the generation of the response function library.