Refining LBM accuracy and efficiency for neutron diffusion: Integrated strategies for model configuration and boundary treatment

Abstract

A solution framework for neutron diffusion equations based on the higher-order lattice Boltzmann method (HLBM) was constructed, with detailed unit conversion procedures for this problem being systematically presented. The influences of relaxation time, discrete velocity models, and boundary condition treatment schemes on numerical performance were comprehensively examined. A nonlinear regulatory relationship between relaxation time and computational domain dimensions was investigated, while the effects of D2Q4, D2Q5, and D2Q9 discrete velocity models on solution accuracy and computational efficiency were comparatively analyzed. A novel boundary condition processing strategy was proposed and validated through comparison with analytical solutions. Research findings indicate that when the relaxation time is set within the range of 1.2 to 1.4, the system achieves the minimum computational error, and the proposed size-dependent dynamic optimization criterion for relaxation time has been proven to effectively reduce computational errors. Regarding discrete models, the D2Q4 model demonstrated superior comprehensive performance, exhibiting 53% and 83% reductions in mean relative errors compared with D2Q9 and D2Q5 models respectively, while achieving 42% faster convergence rates than both counterparts. The novel reflective boundary treatment scheme is demonstrated to exhibit a maximum relative error of 0.13%, while the zero boundary condition treatment scheme achieves a maximum relative error of 0.042%, with no significant increase in computational complexity. The reliability of both schemes is rigorously validated. These research outcomes provide quantitative parameter optimization criteria and innovative boundary treatment schemes for neutron diffusion simulations in nuclear reactors using HLBM, demonstrating significant engineering applicability.