Generation of neutron transport benchmark problems using BEAPAC-3T

A method is described how a quantitative measure can be obtained for the accuracy of numerical methods for the solution of neutron transport problems in an arbitrary homogeneous multidimensional medium. An expansion for the combining coefficients of singular eigenfunctions is developed that yields exact elementary plane-wave solutions that can be evaluated very accurately in terms of exponential integral functions. Linear combinations of these solutions are automatically generated which approximate, in the least squares sense, a user specified incident flux distribution on the boundary of a multidimensional benchmark cell domain. The generated solution is exact for a new benchmark problem which has incident flux given precisely by the generated solution. The quantitative error analysis method has been implemented in the code BEAPAC-3T and is illustrated by application to the TWOTRAN-II code for a square domain problem.