Nuclear Science and Engineering / Volume 155 / Number 1 / January 2007 / Pages 37-52
Most perturbation theory calculation methods for neutron transport problems are based on the assumption that the solution to the adjoint transport problem is known. Here we develop an adjoint transport solution based on the method of cyclic characteristics (MOCC) for two-dimensional fuel assembly problems with isotropic scattering. The main advantages of the MOCC method are (a) it requires lower computing time and memory spaces than the collision probability (CP) method and (b) it does not require the boundary surface currents as for the method of characteristics with isotropic tracking. In the MOCC the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The mathematical relationship between the adjoint function obtained by CP method and the adjoint function by MOCC is also presented. In order to speed up the MOCC solution algorithm, group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. In addition, a combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of large numbers of variables storing tracking-line data and exponential values, is proposed to reduce the computing time. To demonstrate the efficiency of these algorithms, calculations are performed on a 17 × 17 pressurized water reactor lattice, a 37-pin CANDU [Canada deuterium uranium reactor] cell, and the Watanabe-Maynard benchmark. Comparisons of adjoint function and keff results obtained by the MOCC and the CP method are presented.