University of California, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545

Abstract

The purpose of this paper is to present a new technique for accelerating
thermal upscatter source iterations in multigroup neutron transport
calculations. This technique is based upon the use of a one-group diffusion
equation to approximate the multigroup $S_n$ transport equation. It can be
thought of as a *two-grid* technique since the diffusion operator
represents a *coarse-grid* approximation to the transport operator. In
particular, the diffusion operator is coarse with respect to the direction and
energy variables, but it is full-rank with respect to the spatial variables.
Thermal upscatter iterations are often very slow to converge in problems
containing materials such as heavy-water and graphite. For instance, using
infinite-medium Fourier analyses in conjunction with a 69-group neutron
cross-section set having 41 thermal energy groups, we have calculated
unaccelerated spectral radii of 0.9998 and 0.998 for heavy-water and graphite,
respectively. The corresponding accelerated spectral radii are 0.46 and 0.62,
respectively. Thus the spectral radius is dramatically reduced with a single
coarse-grid equation. Computational results are presented which indicate that
our method is both efficient and robust.