Real-time capable three-dimensional heat transfer analysis for hot-rolled heavy plates using a hybrid algebraic multigrid preconditioned conjugate gradient solver

Abstract

Recent heavy plates require precise rolling control due to diversified steel compositions and advanced processing conditions, where accurate temperature prediction is essential. However, three-dimensional transient heat transfer analysis of large-scale heavy plates involves large symmetric positive definite systems with millions of degrees of freedom, limiting computational efficiency for industrial applications. In this study, a high-efficiency three-dimensional transient heat transfer model was developed using a C++ − based Compressed Sparse Row (CSR) data structure and a hybrid Algebraic Multigrid Preconditioned Conjugate Gradient (AMG-PCG) method. The novelty lies in a hybrid multigrid strategy tailored to heavy plate systems. It combines geometry-based multigrid coarsening for efficient C-point selection with algebraic multigrid interpolation to account for anisotropic heat transfer. While pure multigrid methods may suffer from limited convergence due to insufficient representation of physical properties, and pure algebraic multigrid methods incur high computational cost, the proposed approach provided both fast convergence and computational efficiency. The model achieved up to a 99% reduction in solving time compared to conventional methods and converged within 1–2 iterations under identical conditions. Validation using industrial data showed average relative errors below 2.4% for core temperatures and 1.9% for top-surface temperatures. Practical guidelines for mesh distribution and numerical parameter settings based on convergence analysis were systematically established. The model enables accurate real-time temperature prediction and captures full-domain temperature distributions including edge and corner regions, which are difficult to resolve using one- and two-dimensional models. It can serve as an efficient and robust core engine for digital twin and AI-based process control. Copyright