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连续及不连续各向异性热传导问题的数值流形方法求解

刘思敏 张慧华 韩尚宇 刘强

刘思敏, 张慧华, 韩尚宇, 刘强. 连续及不连续各向异性热传导问题的数值流形方法求解[J]. 应用数学和力学, 2020, 41(6): 591-603. doi: 10.21656/1000-0887.400289
引用本文: 刘思敏, 张慧华, 韩尚宇, 刘强. 连续及不连续各向异性热传导问题的数值流形方法求解[J]. 应用数学和力学, 2020, 41(6): 591-603. doi: 10.21656/1000-0887.400289
LIU Simin, ZHANG Huihua, HAN Shangyu, LIU Qiang. Solutions of Continuous and Discontinuous Anisotropic Heat Conduction Problems With the Numerical Manifold Method[J]. Applied Mathematics and Mechanics, 2020, 41(6): 591-603. doi: 10.21656/1000-0887.400289
Citation: LIU Simin, ZHANG Huihua, HAN Shangyu, LIU Qiang. Solutions of Continuous and Discontinuous Anisotropic Heat Conduction Problems With the Numerical Manifold Method[J]. Applied Mathematics and Mechanics, 2020, 41(6): 591-603. doi: 10.21656/1000-0887.400289

连续及不连续各向异性热传导问题的数值流形方法求解

doi: 10.21656/1000-0887.400289
基金项目: 国家自然科学基金(11462014);江西省自然科学基金(20192BAB202001;20151BAB202003);江西省教育厅科学技术研究项目(GJJ180533)
详细信息
    作者简介:

    刘思敏(1996—),女,硕士生(E-mail: liusiminkathy@163.com);张慧华(1982—),男,教授,博士(通讯作者. E-mail: hhzhang@nchu.edu.cn).

  • 中图分类号: TK124

Solutions of Continuous and Discontinuous Anisotropic Heat Conduction Problems With the Numerical Manifold Method

Funds: The National Natural Science Foundation of China(11462014)
  • 摘要: 热传导问题是工程实际中的常见问题.与各向同性材料相比,各向异性材料的热传导更为复杂,因而准确预测其内部的温度分布具有重要的意义.该文发展了一种用于求解典型连续及不连续各向异性稳态热传导问题的数值流形方法(NMM).根据问题的控制微分方程、边界条件以及变分原理,导出了求解此类问题的NMM离散方程.采用独立于物理域所有边界的均匀数学覆盖对几个连续及不连续算例进行了分析,证实了方法的可行性及精度,表明NMM能够很好地模拟各向异性材料的热传导问题.此外,还进一步探讨了材料属性等因素对温度场的影响规律.
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出版历程
  • 收稿日期:  2019-09-25
  • 修回日期:  2019-10-25
  • 刊出日期:  2020-06-01

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