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反演二维瞬态热传导问题随温度变化的导热系数

周焕林 徐兴盛 李秀丽 陈豪龙

周焕林, 徐兴盛, 李秀丽, 陈豪龙. 反演二维瞬态热传导问题随温度变化的导热系数[J]. 应用数学和力学, 2014, 35(12): 1341-1351. doi: 10.3879/j.issn.1000-0887.2014.12.006
引用本文: 周焕林, 徐兴盛, 李秀丽, 陈豪龙. 反演二维瞬态热传导问题随温度变化的导热系数[J]. 应用数学和力学, 2014, 35(12): 1341-1351. doi: 10.3879/j.issn.1000-0887.2014.12.006
ZHOU Huan-lin, XU Xing-sheng, LI Xiu-li, CHEN Hao-long. Identification of Temperature-Dependent Thermal Conductivity for 2-D Transient Heat Conduction Problems[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1341-1351. doi: 10.3879/j.issn.1000-0887.2014.12.006
Citation: ZHOU Huan-lin, XU Xing-sheng, LI Xiu-li, CHEN Hao-long. Identification of Temperature-Dependent Thermal Conductivity for 2-D Transient Heat Conduction Problems[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1341-1351. doi: 10.3879/j.issn.1000-0887.2014.12.006

反演二维瞬态热传导问题随温度变化的导热系数

doi: 10.3879/j.issn.1000-0887.2014.12.006
基金项目: 国家自然科学基金(11072073)
详细信息
    作者简介:

    周焕林(1973—),男,安徽人,教授,博士生导师(通讯作者. E-mail: zhouhl@hfut.edu.cn).

  • 中图分类号: TK124

Identification of Temperature-Dependent Thermal Conductivity for 2-D Transient Heat Conduction Problems

Funds: The National Natural Science Foundation of China(11072073)
  • 摘要: 基于边界元法反演二维瞬态热传导问题随温度变化的导热系数.采用Kirchhoff变换将非线性的控制方程转变为线性方程.边界元法用于构建二维瞬态热传导问题的数值分析模型.将反演参数作为优化变量,测点温度计算值与测量值之间的残差平方和作为优化目标函数.引入复变量求导法求解目标函数的梯度矩阵,梯度正则化法用于优化目标函数获得反演结果.探讨时间步长、测点数量和随机偏差对反演结果的影响.减小步长、增加测点数量收敛速度加快.降低了随机偏差,计算结果更精确.算例证明了算法的有效性与稳定性.
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出版历程
  • 收稿日期:  2014-07-23
  • 修回日期:  2014-10-25
  • 刊出日期:  2014-12-15

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