A numerical stabilization model for the half-boundary method in solving heat conduction problems

The half-boundary method (HBM), an extension of the boundary element method, demonstrates superior accuracy and computational efficiency in nuclear fuel rod heat transfer simulations. However, its numerical stability under inappropriate time steps and iteration schemes remains unresolved, a problem systematically addressed in this work for the first time. Von Neumann analysis reveals that temporal stability requires the implicit weighting parameter θ of time discretization scheme to exceed 0.5. Spectral radius analysis for spatial iteration indicates stability in steady-state but instability in transient-state conditions. To address spatial instability, we analyze error amplification mechanisms and propose a stabilization model that maps acceptable error thresholds to time step sizes, thereby ensuring stable spatial iterations. Our analysis further demonstrates that computational stability improves as the mesh Fourier number deviates from unstable ranges. The proposed model is successfully validated through application to realistic nuclear fuel rod heat conduction problems.