Improved adaptive Wielandt acceleration method for solving neutron diffusion equation under extremely-distorted flux condition

Stable and efficient approach for solving neutron diffusion equation is essential for reactor core safety analysis, particularly under control rod configurations with characteristic of extremely-distorted neutron-flux distributions. Conventional Wielandt acceleration method improves convergence rate of power iteration but often results in ill-conditioned response matrices in such cases, causing numerical instability or non-physical solutions. To address this limitation, this study develops an improved adaptive Wielandt acceleration method that incorporates segmented error amplification factors and self-correction mechanism for the threshold shift parameter. The method has been implemented in the core physics code SPARK and evaluated using one-rod-out ( N -1) and two-rod-out ( N -2) configuration problems for both the rectangular-assembly reactor M310 and hexagonal-assembly reactor VVER-1000. Numerical verification demonstrates that the newly proposed adaptive scheme eliminates parameter forbidden zones, reduces the need for negative flux corrections, and achieves higher numerical stability compared with the conventional approach. In terms of computational efficiency, the proposed method consistently outperforms the conventional Wielandt acceleration, reaching acceleration ratios of 3.10∼8.51 and 5.41∼6.80 for the VVER-1000 and M310 cases, respectively, compared with 2.17∼8.24 and 2.53∼5.69 for the conventional method. Overall, the improved adaptive Wielandt acceleration provides a robust and efficient framework for large-scale reactor core simulations under extremely-distorted neutron-flux distributions, offering practical benefits for nuclear design and safety analysis.