Review of the Discrete-Ordinates Method for Particle Transport in Nuclear Energy

The advantages and recent advancements of the Discrete-Ordinates (SN) Method have established its widespread adoption in particle transport calculations for nuclear energy systems. The mathematical foundations and diverse applications of the SN method are comprehensively summarized in this review. Recent advances are critically evaluated, with particular emphasis placed on advanced discretization techniques, high-performance computing implementations, and hybrid coupling strategies with MC, MOC method, and so on. Despite these developments, challenges remain, including the need for high-fidelity simulations, optimization of computational performance, and the complexity introduced by temporal dependencies in dynamic radiation field calculations, which necessitates innovative numerical methods. Future developments of the SN method are anticipated to address these challenges through enhanced high-fidelity numerical simulation, robust high-performance computing frameworks, multi-physics field coupling, and AI integration. These developments advance the industrial-scale implementation of the SN method in nuclear energy applications, enabling efficient and accurate analyses of complex reactor systems.