Discrete Elements Method of Neutron Transport

A new neutron transport method, called discrete elements (L_N), is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation.The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The zeroth and first angular moments of the directional flux, over each element, are estimated by numerical quadrature and yield a flux-weighted average streaming direction for the element. Data for this estimation are fluxes infixed directions calculated as in S_N. The spatial quadrature then propagates the element flux in this “steered” direction, strongly ameliorating ray effect. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L_N method is more consistently convergent toward a Monte Carlo benchmark solution.