An Efficient Element-Free Galerkin Method Based on Adaptive TR-AB2 Scheme for Transient Heat Conduction Problems

被引：0

作者：

Xiang, Shuyi ^{[1
]}

Zhang, Xiaohua ^{[2
]}

机构：

[1] College of Science, China Three Gorges University, Yichang,443002, China

[2] School of Mathematics, Yunnan Normal University, Kunming,650500, China

来源：

IAENG International Journal of Applied Mathematics | 2023年 / 53卷 / 04期

关键词：

Computational mechanics - Galerkin methods - Heat conduction - Numerical methods;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Meshless methods have numerous advantages over mesh-based approaches, but their high computational cost has significantly hindered their progress, particularly for time-dependent problems. In this study, we propose a time-adaptive meshless approach aimed at improving the computational efficiency of the method for addressing time-dependent issues. Specifically, we use the element-free Galerkin (EFG) method for spatial discretization, and the trapezoidal rule (TR) with adaptive time stepping for time integration. Additionally, we incorporate the explicit second-order Adams-Bashforth (AB2) method to control the error. The adaptive control of the time step effectively resolves issues related to non-convergence and low computational efficiency caused by inappropriate selection of the time step. To validate the efficacy and accuracy of the algorithm, we provide several numerical examples. The numerical results demonstrate that the EFG method combined with TR-AB2 method (EFG-TR-AB2) exhibits significant potential in solving two-dimensional transient heat conduction problems, which can maintain computational accuracy and improve computational efficiency. © (2023), (International Association of Engineers). All Rights Reserved.

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