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有限元法求解瞬态温度场时的数值振荡研究

刘文胜 李璇 马运柱 杨肃

刘文胜, 李璇, 马运柱, 杨肃. 有限元法求解瞬态温度场时的数值振荡研究[J]. 应用数学和力学, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166
引用本文: 刘文胜, 李璇, 马运柱, 杨肃. 有限元法求解瞬态温度场时的数值振荡研究[J]. 应用数学和力学, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166
LIU Wensheng, LIXuan, MA Yunzhu, YANG Su. Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method[J]. Applied Mathematics and Mechanics, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166
Citation: LIU Wensheng, LIXuan, MA Yunzhu, YANG Su. Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method[J]. Applied Mathematics and Mechanics, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166

有限元法求解瞬态温度场时的数值振荡研究

doi: 10.21656/1000-0887.380166
基金项目: 国家高技术研究发展计划(863计划)(2009AA034300)
详细信息
    作者简介:

    刘文胜(1967—),男,教授,博士生导师;马运柱(1975—),男,教授,博士生导师(通讯作者. E-mail: yangsupm@csu.edu.cn).

  • 中图分类号: TK124

Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

Funds: The National High-tech R&D Program of China (863 Program) (2009AA034300)
  • 摘要: 针对有限元求解瞬态温度场时解的振荡问题,通过对热传导矩阵和热容矩阵的分析,研究了数值仿真中解的振荡原因以及消除振荡的方法.研究结果表明,热传导矩阵违反了热力学第二定律以及在迭代初期,协调热容矩阵的单元内温度变化率的连续性假设与实际偏差很大是产生数值振荡的原因.规范单元形状和采用适当的集中热容矩阵,可以有效消除数值振荡.同时,以无限大平板传热过程为背景,通过不同计算方法的对比,验证分析了结论.
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出版历程
  • 收稿日期:  2017-06-13
  • 修回日期:  2017-09-25
  • 刊出日期:  2018-04-15

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