Zonal free element method for solving nonlinear transient heat conduction problems

This paper develops the Zonal Free Element Method (ZFREM) to solve transient nonlinear heat conduction problems. As a novel meshless method, ZFREM utilizes the shape functions of isoparametric elements, which contribute to its enhanced stability compared to other meshless methods. Moreover, through domain partitioning, this method effectively handles complex geometric configurations. Another distinguishing feature is that element is formed by the collocation node (CN) and nodes around it (field nodes), which makes it easy to use high-order elements and obtain more accurate solutions. The paper also establishes a specific unified format for solving nonlinear heat conduction problems using this method. Finally, the authors used the proposed method to analyze three-dimensional unsteady heat conduction problems involving nonlinear thermal conductivity. The results obtained using the proposed method are in agreement with reference results, validating its effectiveness.