Nuclear Science and Engineering / Volume 159 / Number 2 / June 2008 / Pages 169-181
A new benchmark for monoenergetic neutron transport in one-dimensional cylindrical geometry is presented. In the past, several accurate benchmarks (i.e., numerical solutions) in cylindrical geometry, based on the singular eigenfunction expansion of the solution to the corresponding pseudoproblem, have appeared in the literature. In the new formulation, called the direct FN method in cylindrical geometry, we base the FN solution directly on the integro-differential equation satisfied by the pseudoproblem. Through appropriate projections, a straightforward FN formulation results in singular integral equations for both the flux and current. Enhanced by convergence acceleration, the FN approximation accurately reproduces published benchmark solutions for both fixed sources and criticality. Thus, we have developed an entirely pedagogical self-contained and highly accurate benchmark based on an alternative application of FN theory.