A new procedure for solving neutron transfer problems

In this paper, we propose an accurate and efficient procedure named half boundary method (HBM) to solve one-dimensional neutron transfer problems. In the process of solving the Boltzmann transfer equation, the relationships between every two neighboring nodes are solved first. Then, starting from a vacuum boundary, the neighboring relationships are iteratively applied to solve the neutron distribution. In two reflective boundaries problems, the reflective boundaries are applied to solve the neutron flux at the boundaries first, then the neutron distribution is solved similar to the vacuum boundary problems. Different from the traditional method, no matter how many segments are dispersed, at most two-order matrixes are involved in HBM calculations. So, HBM shows great potential in saving computational memory, particularly for problems with huge girds. In this paper, we introduce the fundamental theory and investigate the applicability, accuracy, and efficiency of HBM by solving five examples with different situations and boundaries.