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

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

南昌航空大学土木建筑学院, 南昌 330063

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
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- 文章访问数: 1364
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- 被引次数: 0
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

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

School of Civil Engineering and Architecture, Nanchang Hangkong University, Nanchang 330063, P.R.China

Funds: The National Natural Science Foundation of China(11462014)

摘要

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.
- 各向异性 /
- 稳态热传导 /
- 数值流形方法 /
- 温度 /
- 连续及不连续问题
Abstract: The heat conduction is a common problem in engineering practice. Compared with those of isotropic materials, the heat conduction problem of anisotropic materials is more complicated, so it is of great significance to accurately predict the internal temperature distribution. The numerical manifold method (NMM) was developed to solve typical continuous and discontinuous heat conduction problems in anisotropic materials. According to the governing differential equation, boundary conditions and variational principles, the NMM discrete equations for such problems were derived. Several representative examples involving continuous and discontinuous situations were analyzed with the uniform mathematical cover independent of all physical boundaries. The results prove the feasibility and accuracy of the method and indicate that the NMM can simulate the heat conduction problem of anisotropic materials well. Besides, the influences of the material properties and crack configurations on the temperatures were also investigated.
- anisotropic /
- steady heat conduction /
- numerical manifold method /
- temperature /
- continuous and discontinuous problem

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参考文献(25)

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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

doi: 10.21656/1000-0887.400289

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）.

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

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留言板

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

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）.

计量

出版历程

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

计量

出版历程

目录

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）.