Enhanced discrete element methods for neutron transport

Angular approximation techniques to the Boltzmann transport equation have been developed that are accurate and efficient either near material interfaces or deep within materials. In this research, the traditional discrete element method is modified to accurately and efficiently approximate the solution of the single energy, time-independent, slab geometry transport equation both near material interfaces and deep within a material. The ordinates used in the streaming term are scaled based on the material scattering ratio to capture the fundamental transport mode for the material. These scaled ordinates accurately capture the attenuation of the solution deep within a material with a minimum number of elements. Near an interface a large number of elements must be used to capture the complicated flux behavior. Transitioning between a large number of elements near the interface and a minimum number of elements far from the interface is a straightforward process of joining and partitioning discrete elements. This multiple resolution discrete elements technique of having many elements near an interface and a few elements far from the interface that use scaled ordinates based on the material scattering ratio is shown to accurately and efficiently capture the solution throughout a material.