On the Application of the Discrete Ordinates Method to Fixed-Source Problems (Forward and Adjoint)

摘要

This paper has demonstrated that the SN orderrequired for convergence of the neutron leakage from asphere with an intrinsic (internal) source is greater thanthat required to compute keff for the same sphere. It is wellknown that the keff eigenvalue converges faster than theeigenfunction (angular flux) associated with it [1]. It isimportant to avoid being seduced by the ease ofconverging keff.This study shows that poor convergence may bediagnosed by comparing forward and adjoint results forthe same quantity. (Poor convergence may also bediagnosed using the methods of Azmy [10].) Anyinconsistency between forward and adjoint solutions willadversely affect the accuracy of quantities relying onforward-adjoint inner products, such as sensitivities.These results are relevant for nonproliferationproblems and indeed any problem for which the responseis a functional of the local flux.