Efficient Time-Stepping Methods for Isogeometric Analysis of Nonlinear Heat Conduction in Composites

In this paper, we propose a class of high-order time integration schemes combined with high-order IsoGeometric Analysis (IGA) in three space dimensions. The combined methods offer robust solutions of nonlinear heat diffusion in three-dimensional composites that pose numerical challenges. This tailored strategy significantly enhances computational efficiency, especially crucial when addressing nonlinear heat transfer in three-dimensional enclosures. Leveraging precise geometry representation and seamless high-order element continuity of the IGA, this method effectively exploits these advantages. It emphasizes the vital synergy between high-order spatial discretization and an equivalent high-order time integration scheme. This study also highlights the risks of overlooking this pairing, which can lead to a degradation of the overall high-order accuracy and increased computational demands due to the complexity of high-order nonuniform rational B-splines. Numerical examples, such as applications involving a furnace wall segment and a rail wheel heat transfer, are used to validate the efficiency and accuracy of the combined approach. Consistently surpassing the conventional methods in both aspects, the proposed method notably excels in providing precise solutions for steep heat gradients even on coarse meshes. Consequently, this approach constitutes a substantial advancement in the field of transient heat transfer analysis within composite domains.