Application of the half-boundary method to solving the neutron transport equation in 1D cylindrical coordinate

The neutron distribution within a nuclear reactor core plays a crucial role in nuclear engineering, directly influencing the safe operation of nuclear reactors. The neutron transport equation provides a fundamental approach to determine this distribution. This study applies the half-boundary method (HBM) to solve the neutron transport equation in cylindrical coordinates. By deriving mathematical relationships among discrete nodal values, the HBM establishes explicit correlations between boundary conditions and neutron flux at arbitrary spatial points throughout the model. Compared to traditional finite difference methods, the HBM only requires iterative calculations on boundary values, thereby improving computational accuracy while reducing both execution time and memory requirements. In this paper, the HBM discretization and derivation processes are described in detail. The sensitivity analysis to assess the influence of varying the spatial and angular discretization parameters is made. Convergence analysis demonstrates that spatial discretization achieves second-order accuracy in the radial direction, while angular discretization exhibits first-order convergence. Three numerical test cases are presented to verify the HBM by comparing its results with the Monte Carlo method, showing their consistency, high accuracy, and credibility.