Pseudo-point transport technique : a new method for solving the Boltzmann transport equation in media with highly fluctuating cross sections

A new method for solving radiation transport problems is presented. The heart of the technique is a new cross section processing procedure for the calculation of group-to-point and point-to-group cross sections sets. The method is ideally suited for problems which involve media with highly fluctuating cross sections, where the results of the traditional multigroup calculations are beclouded by the group averaging procedures employed. Extensive computational efforts which would be required to numerically evaluate double integrals in the multigroup treatment, prohibit iteration to optimize the energy boundaries. On the other hand, use of point-to-point techniques (as in the stochastic technique) is often prohibitively expensive due to the large computer storage requirement.

The pseudo-point code is a hybrid of the two aforementioned methods (group-to-group and point-to-point), hence the name pseudo-point; which reduces the computational efforts of the former and the large core requirement of the latter. The pseudo-point code generates the groupto-point or the point-to-group transfer matrices and can be coupled with the existing transport codes to calculate pointwise energy-dependent fluxes. This approach yields much more detail than is available from the conventional energy-group treatments. Due to the speed of this code, several iterations could be performed (in affordable computing efforts) to optimize the energy boundaries and the weighting functions.

The pseudo-point technique is demonstrated by solving six problems, each depicting a certain aspect of the technique. The results are presented as flux vs. energy at various spatial intervals. The sensitivity of the technique to the energy grid and the savings in computational effort are clearly demonstrated.