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一种基于新型插值单元的稳态传热边界元法

侯俊剑 郭壮志 钟玉东 何文斌 周放 谢贵重

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 doi: 10.21656/1000-0887.410394
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 doi: 10.21656/1000-0887.410394
HOU Junjian, GUO Zhuangzhi, ZHONG Yudong, HE Wenbin, ZHOU Fang, XIE Guizhong. A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1169-1176. doi: 10.21656/1000-0887.410394
Citation: HOU Junjian, GUO Zhuangzhi, ZHONG Yudong, HE Wenbin, ZHOU Fang, XIE Guizhong. A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1169-1176. doi: 10.21656/1000-0887.410394

一种基于新型插值单元的稳态传热边界元法

doi: 10.21656/1000-0887.410394
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)
详细信息
    作者简介:

    侯俊剑(1982—),男,副教授,博士(E-mail:houjunjian@zzuli.edu.cn)

    钟玉东(1990—),男,讲师,博士(通讯作者. E-mail:zhongyd@zzuli.edu.cn)

  • 中图分类号: O343

A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements

  • 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。
  • 图  1  新型插值单元

    Figure  1.  New interpolation elements

    图  2  新型单元用于插值已知边界变量

    Figure  2.  The novel elements used for interpolation of the known boundary variables

    图  3  新型单元用于插值未知边界变量

    Figure  3.  The novel elements used for interpolation of the unknown boundary variables

    图  4  新型单元用于插值非连续边界变量

    Figure  4.  The novel elements used for interpolation of the discontinuous boundary variables

    图  5  带孔平板的几何模型(单位:mm)

    Figure  5.  The geometric model for the plate with a hole (unit: mm)

    图  6  底边上的热流密度q的数值结果

    Figure  6.  The numerical results of thermal flux on the bottom edge

    图  7  内孔边界上热流量q的数值结果

    Figure  7.  The numerical results of thermal flux on the boundary of the internal hole

    图  8  底边和侧边界上热流量q的相对误差和收敛性图

    Figure  8.  The relative errors and convergence rates of q on the bottom and side edges

    图  9  复合支架的几何模型(单位:m)

    Figure  9.  The geometric model for a composite bracket(unit: m)

    图  10  复合支架所施加的混合边界条件

    Figure  10.  The mixed boundary conditions applied for the composite bracket

    图  11  左侧边界和圆弧边界(R=0.5 m)上温度的计算结果

    Figure  11.  The computational results of temperature on left and arc (R=0.5 m) boundaries

    图  12  本文方法计算得到的温度云图

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本。

    Figure  12.  The temperature nephogram obtained with the proposed method

    图  13  有限元法参考解:温度云图

    Figure  13.  The reference solution of the temperature nephogram with the finite element method

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出版历程
  • 收稿日期:  2020-12-24
  • 修回日期:  2021-05-07
  • 网络出版日期:  2021-12-07
  • 刊出日期:  2021-11-30

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