Reconstruction and Numerical Implementation of High Burn-up Structure Pore Evolution Model for UO₂ Fuel

High burn-up structure (HBS) is a typical microstructural feature in high burn-up UO₂ fuel, and its pore evolution strongly affects local porosity development, fission-gas redistribution, and the performance of irradiated fuel under normal and accident conditions. Existing reduced-order descriptions used in fuel performance analysis often rely on empirical thresholds or simplified kinetics, so they do not fully capture the dynamic competition among pore nucleation, gas capture, heterogeneous re-solution, and grain-boundary accumulation. A second-order Fokker-Planck approximation has been proposed in previous work to reduce the infinite-dimensional cluster-dynamics description to a tractable moment system. However, the original reduced formulation still suffers from incomplete conservation treatment and poor robustness. Such issues particularly arise when strongly nonlinear coupling terms are integrated on coarse engineering time steps. The present study aims to reconstruct an HBS pore evolution model based on a second-order Fokker-Planck approximation and to develop a more self-consistent numerical treatment for pore number density, pore size, and fission-gas redistribution in HBS regions. The model was reformulated from the mesoscopic governing equation of HBS pore evolution. A continuous Fokker-Planck-type approximation was introduced around the mean pore size, and the size-dependent rate terms were expanded to second order. The resulting weighted summation of the discrete master equation yielded a set of moment equations up to second order for pore number density, mean atom content, and variance-related quantities. In this reconstruction, the depletion term associated with heterogeneous re-solution was retained explicitly in the evolution equation. Consequently, local mass conservation and dimensional consistency were recovered in the reconstructed formulation. The pore-volume evolution law was then coupled with the internal gas pressure and mechanical equilibrium of spherical pores. The pore pressure was evaluated through the Carnahan-Starling hard-sphere equation of state, and vacancy absorption or emission was linked to the pressure deviation from equilibrium. Pore interconnection and its feedback on the effective evolution of the pore population were also incorporated. For numerical implementation, an operator-splitting framework and a semi-implicit treatment were adopted to handle the stiffness induced by pore growth and interconnection. Additionally, substep integration was used to improve robustness during coupling with coarse external time steps. The reconstructed model now gives a physically clearer and numerically more stable description of HBS pore kinetics. Comparison with experimental observations and predictions from the baseline code shows that the model successfully reproduces the characteristic rise-and-fall trend of pore number density with increasing effective burn-up and the continuous coarsening of the average pore radius. It also captures a characteristic feature of HBS, namely the depletion of intragranular xenon and the accumulation of submicron pores at grain boundaries. These results indicate that the reduced-order formulation preserves the key mesoscopic signatures of HBS evolution while remaining applicable to engineering-scale fuel performance calculations. In addition, the simulations reveal the coupled evolution of porosity, pore number density, and pore size in HBS regions, helping to clarify how grain-boundary-dominated pore growth develops under high burn-up conditions. Overall, the reconstructed model provides a more reliable kinetic framework for HBS grain-boundary pore evolution than conventional reduced descriptions. The formulation still reflects the simplifying assumptions inherent in the present reduced-order treatment, but it establishes an essential dynamic backbone for mechanistic analysis of HBS pore evolution. The model therefore provides useful support for the design optimization of high burn-up fuel, for safety assessment under accident conditions, and for future multi-scale coupling in advanced fuel performance codes.