Central-Difference method based on consistent Half-Node linear approximation for the neutron diffusion equation

The finite difference method (FDM) is widely used in the numerical solution of the neutron transport equation due to its simplicity and ease of parallelization. However, inconsistent theoretical approximations appear in the conventional central difference method, which limits its accuracy and efficiency. A half-node linear approximation is employed for the leakage term, while a full-mesh linear approximation is applied to the collision and source terms.To eliminate this inconsistency, a Central Finite Difference Method based on a Consistent Half-node Linear approximation, named as HNL-CFDM is proposed in the paper. By adopting a consistent half-node linear approximation across all terms of the diffusion equation, this method ensures that the discrete formulation remains highly aligned with the physical essence of the continuous equation, thereby effectively enhancing spatial accuracy. In addition, to address the issue of slow convergence in large sparse linear systems often encountered in high-fidelity full-core calculations with this new scheme, a hybrid acceleration strategy combining Coarse Mesh Rebalance (CMR) and the Gauss-Seidel Left-preconditioned Generalized Minimal Residual method (gsl-GMRES) are developed.The performance of the proposed method was validated using the KAIST benchmark problems. Numerical results demonstrate that, compared to the FDM, the HNL-CFDM scheme achieves a nearly twofold improvement in the accuracy at the minimal cost of only a 7% increase in computation time. Furthermore, regarding iterative acceleration, the hybrid scheme achieves an acceleration ratio of approximately 12 times compared to the traditional Gauss-Seidel (GS) iteration method.This study confirms that the proposed method greatly improves the accuracy of neutron diffusion calculations while maintaining computational efficiency, providing a more reliable numerical tool for reactor physics analysis.