Accelerated solution methods for self-adjoint angular flux neutron transport equations based on scattering matrix decoupling

Advanced microreactors exhibit compact geometries, elevated neutron leakage, and pronounced anisotropic scattering. These characteristics necessitate high-fidelity neutron transport methods to accurately resolve core flux distributions. The neutron transport equation, a seven-dimensional integro-differential equation, poses significant computational challenges in numerical solutions. Conventional acceleration techniques, such as coarse mesh finite difference and diffusion-synthesis acceleration, are widely employed to improve the efficiency of neutron transport codes. However, these approaches often require reformulation of the governing equations or introduce substantial approximations, potentially compromising solution accuracy. To address these limitations, this work introduces a scattering matrix decoupling (SMD) method within the iterative solver framework. This method is designed to reduce computational cost and enhance the overall efficiency of the iterative process in the neutron transport equation. The performance of the SMD method is validated against established neutron transport benchmarks: the strong scattering problem, the IAEA PWR, the gadolinium-bearing BWR, and the KUCA reactor. Results indicate that the effective multiplication factor (keff) and neutron flux distributions remain unchanged with or without the application of SMD, confirming the algorithmic correctness of the implementation. Analysis of the benchmark cases reveals that the SMD method accelerates computation by 86.5%, 43.6%, 45.3%, and 71.6% for the strong scattering problem, the IAEA PWR, the gadolinium-bearing BWR, and the KUCA reactor respectively. Furthermore, the acceleration efficiency scales with problem size, achieving greater speedup in systems with higher degrees of freedom.