A boundary-type algorithm based on the discrete ordinates for neutron transport equation

The spatial distribution of neutron flux in the core of a nuclear reactor plays a crucial role in ensuring nuclear safety. It can be determined by solving the neutron transport equation, where computational resource consumption is gradually receiving more attention, especially in problems with multiple reflective boundary conditions. It is common practice to assume initial boundary values in one angular direction to obtain a global solution, and then use reflective boundary conditions to solve for the other directions, iterating until convergence. However, this approach has the drawback of requiring the global solution, and each iteration necessitates storing the neutron flux values, consuming time and storage space. In order to address this issue, this paper proposes a precise and efficient boundary-type method, the Half Boundary Method (HBM). This method establishes relationships between adjacent node values through integration and mathematical deduction, ultimately obtaining the relationship among any node and the boundary values in any direction. As a result, iteration is only required for boundary values, reducing the iteration amount and thus saving time and storage space. Using the discrete ordinate (S_N) method for angular discretization and HBM for spatial discretization, this paper solved the steady-state neutron transport equation for two-dimensional systems modeled with Cartesian geometry. The method is validated using several benchmark problems, including the 2D ISSA benchmark, the 2D mono-group k-eigenvalue problem and BWR rod bundle test problem. All of these problems demonstrate good results and effectively reduced computational time.