A novel efficient method for transient heat analysis of cylindrical periodic structure based on the physical features and group theory

In this paper, a novel efficient and accurate numerical method is developed for analyzing the transient temperature responses of cylindrical periodic structures. By exploiting the structure's circumferential cyclic periodic property and leveraging group theory, a circumferential decomposition strategy is presented to transform the temperature response analysis of the cylindrical periodic structure into the analyses of a series of one-dimensional periodic structures. Then, based on the physical nature of the transient heat conduction, an axial decomposition strategy is developed to convert the computations of the temperatures of these one-dimensional periodic structures into the calculations of the temperatures of a series of small-scale structures. The computational cost of these small-scale structures is further reduced by using the group theory. Several numerical examples demonstrate that the proposed method has higher accuracy and computational efficiency in comparison with the Crank-Nicolson method. When the Crank-Nicolson method attains the acceptable results, the proposed method is about 10 and 20 times faster than the Crank-Nicolson method with direct and preconditioning conjugate gradient solvers, respectively.