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瞬态热传导的奇异边界法及其MATLAB实现

李煜冬 王发杰 陈文

李煜冬, 王发杰, 陈文. 瞬态热传导的奇异边界法及其MATLAB实现[J]. 应用数学和力学, 2019, 40(3): 259-268. doi: 10.21656/1000-0887.390225
引用本文: 李煜冬, 王发杰, 陈文. 瞬态热传导的奇异边界法及其MATLAB实现[J]. 应用数学和力学, 2019, 40(3): 259-268. doi: 10.21656/1000-0887.390225
LI Yudong, WANG Fajie, CHEN Wen. MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction[J]. Applied Mathematics and Mechanics, 2019, 40(3): 259-268. doi: 10.21656/1000-0887.390225
Citation: LI Yudong, WANG Fajie, CHEN Wen. MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction[J]. Applied Mathematics and Mechanics, 2019, 40(3): 259-268. doi: 10.21656/1000-0887.390225

瞬态热传导的奇异边界法及其MATLAB实现

doi: 10.21656/1000-0887.390225
基金项目: 国家自然科学基金(11802151;11572111;11372097)
详细信息
    作者简介:

    李煜冬(1997—),男,硕士(E-mail: 863949642@qq.com);王发杰(1986—),男,副教授,博士(E-mail: wfj1218@126.com);陈文(1967—2018),男,教授,博士,博士生导师(通讯作者. E-mail: chenwen@hhu.edu.cn).

  • 中图分类号: O302

MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction

Funds: The National Natural Science Foundation of China(11802151;11572111;11372097)
  • 摘要: 基于动力学问题时间依赖基本解的奇异边界法是一种无网格边界配点法.该方法引入源点强度因子的概念从而避免了基本解的源点奇异性,具有数学简单、编程容易、精度高等优点.将该方法用于瞬态热传导问题的数值模拟,运用MATLAB实现该问题的数值研究,并创建相应的MATLAB工具箱.针对二维和三维瞬态热传导问题,进行了基于反插值技术和经验公式的奇异边界法MATLAB算例实现.针对支撑圆坯低温瞬态温度场的模拟结果表明,瞬态热传导奇异边界法的MATLAB工具箱具有简单、方便、精确可靠的优点.研究成果有助于发展瞬态热传导的奇异边界法,并为瞬态热传导问题的数值分析和仿真提供了一种简单高效的模拟工具.
  • [1] 赵金军, 彭海峰, 原志超. 三维变系数热传导问题边界元分析中几乎奇异积分计算[J]. 计算力学学报, 2015,32(1): 7-13.(ZHAO Jinjun, PENG Haifeng, YUAN Zhichao. Evaluation of nearly singular integrals in boundary element analysis of 3D heat conduction problem with variable coefficients[J]. Chinese Journal of Computational Mechanics,2015,32(1): 7-13.(in Chinese))
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    [3] 李庆华, 陈莘莘. 基于无网格自然邻接点Petrov-Galerkin法求解带源参数瞬态热传导问题[J]. 动力学与控制学报, 2014,12(2): 178-182.(LI Qinghua, CHEN Shenshen. Analysis of transient heat conduction problems with a source parameter based on meshless natural neighbour Petrov-Galerkin method[J]. Journal of Dynamics and Control,2014,12(2): 178-182.(in Chinese))
    [4] 陈豪龙, 周焕林, 余波. 瞬态热传导问题的精细积分-双重互易边界元法[J]. 应用力学学报, 2017,34(5): 835-841.(CHEN Haolong, ZHOU Huanlin, YU Bo. Precise integration DRBEM for solving transient heat conduction problems[J]. Chinese Journal of Applied Mechanics,2017,34(5): 835-841.(in Chinese))
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出版历程
  • 收稿日期:  2018-08-27
  • 修回日期:  2018-09-16
  • 刊出日期:  2019-03-01

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