2. Steady-State Neutron Transport Theory and Simulation

Neutron transport theory is the research basis for neutronics and focuses on the description of neutron motion in media and the corresponding laws. There are two types of methods for neutron transport calculation: the Monte Carlo method (also called the probabilistic method or the stochastic method) and the deterministic method. The Monte Carlo method is a numerical method based on probability and statistical theories, and can explicitly describe the characteristics of randomly moving particles and the process of physical experiments. In contrast, in the deterministic method, a group of mathematical–physical equations are first built up to explain the physical characteristics of the target system. Then, by discretizing the variables in these equations, including direction, energy, space, and time, an approximate solution can be obtained with numerical calculation. There are complicated features for advanced nuclear systems, such as the complex neutron spectrum and angular distribution, complicated material composition, large spatial span, complex geometry, etc. The Monte Carlo method uses the continuous-energy cross section, and can be used to address any complex geometry, with prominent advantages for neutron transport simulations for advanced nuclear systems. However, some challenges, such as the slow convergence rate and difficulty in addressing problems of deep penetration, still exist. The deterministic method is faster, but falls short in addressing advanced nuclear systems with complex geometries, strong anisotropy of neutron scattering, and complicated energy spectrums. In recent years, the method of characteristics (MOC) and the discrete ordinates method with unstructured meshes have been developed with improved geometry processing abilities. However, problems, such as the ray effects and the high cost of large-scale systems, still need to be solved. The Monte Carlo–deterministic coupling method, which combines the advantages of both the Monte Carlo and deterministic methods, is one of the most efficient and accurate methods for solving transport problems in advanced nuclear systems.