| 一种基于新型插值单元的稳态传热边界元法 |
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| 引用本文： | 侯俊剑,郭壮志,钟玉东,何文斌,周放,谢贵重.一种基于新型插值单元的稳态传热边界元法[J].应用数学和力学,2021,42(11):1169-1176. |
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| 作者姓名： | 侯俊剑 郭壮志 钟玉东 何文斌 周放 谢贵重 |
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| 作者单位： | 1.郑州轻工业大学 机电工程学院，郑州 450002 |
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| 基金项目： | 河南省高等学校青年骨干教师培养计划(2019GGJS130)；河南省科技攻关项目(202102210290)；河南省高等学校重点科研资助项目(21A460029；21A460030) |
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| 摘 要： | 为了提高边界元法在求解稳态热问题时的计算精度,通过使用一种新型单元插值方法(称为扩展单元插值法)，实现对稳态传热问题的求解。扩展单元是在传统不连续单元的边界配置虚拟节点，把原非连续单元变成高阶的连续单元，并将其作为新型的插值单元。利用虚拟节点和内部源节点构造出的插值函数，可以精确插值边界上的连续和不连续物理场，插值精度要比原始不连续单元高两阶。另外，边界积分方程只在传统的不连续单元的内部节点处建立，只包含内部源节点的自由度，而虚拟节点的自由度可通过与内部源节点之间的关系消除掉，因此最终系统方程的求解规模不会增加。这种新型的插值单元继承了传统连续和不连续单元的优点，克服了它们的缺点。数值结果表明，此种单元插值方法用于求解稳态传热问题时可获得较高的计算精度和收敛性。
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| 关 键 词： | 边界元法 边界积分方程 稳态传热 插值单元 |
| 收稿时间： | 2020-12-24 |
A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements |
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| Affiliation: | 1.College of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, P.R.China2.Henan Engineering Research Center of New Energy Vehicle Lightweight Design and Manufacturing, Zhengzhou 450002, P.R.China |
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| Abstract: | To improve the computational accuracy of the boundary element method (BEM) for solving the steady-state heat problems, a new method was studied with a new element interpolation method (called expansion element interpolation method). The novel expansion interpolation element was obtained through configuration of virtual nodes at the boundary of the traditional discontinuous element, to transform the original discontinuous element into a higher-order continuous element. The interpolation function constructed with the virtual node and the internal source node can accurately work in the continuous and discontinuous physical fields on the boundary, and the interpolation accuracy increases by 2 orders compared with that of the original discontinuous element. In addition, the boundary integral equation is only valid at the internal source nodes of the traditional discontinuous element and contains only the degrees of freedom of the source nodes, while the degrees of freedom of the virtual node can be eliminated through the relationship between the virtual node and the internal source node, so the size of the final linear system equations will not increase. This new interpolation element inherits the advantages of the traditional continuous and discontinuous elements and overcomes their disadvantages. The numerical results show that, the proposed method helps solve the steady-state heat transfer problem with high computational accuracy and convergence. |
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