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

The advantages and recent advancements of the Discrete-Ordinates (S N ) Method have established its widespread adoption in particle transport calculations for nuclear energy systems. The mathematical foundations and diverse applications of the S N 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 S N 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 S N method in nuclear energy applications, enabling efficient and accurate analyses of complex reactor systems.