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基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

朱强华 杨恺 梁钰 高效伟

朱强华, 杨恺, 梁钰, 高效伟. 基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法[J]. 力学学报, 2020, 52(1): 124-138. doi: 10.6052/0459-1879-19-323
引用本文: 朱强华, 杨恺, 梁钰, 高效伟. 基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法[J]. 力学学报, 2020, 52(1): 124-138. doi: 10.6052/0459-1879-19-323
Zhu Qianghua, Yang Kai, Liang Yu, Gao Xiaowei. A NOVEL FAST ALGORITHM BASED ON MODEL ORDER REDUCTION FOR ONE CLASS OF TRANSIENT NONLINEAR HEAT CONDUCTION PROBLEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 124-138. doi: 10.6052/0459-1879-19-323
Citation: Zhu Qianghua, Yang Kai, Liang Yu, Gao Xiaowei. A NOVEL FAST ALGORITHM BASED ON MODEL ORDER REDUCTION FOR ONE CLASS OF TRANSIENT NONLINEAR HEAT CONDUCTION PROBLEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 124-138. doi: 10.6052/0459-1879-19-323

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

doi: 10.6052/0459-1879-19-323
基金项目: 1) 中央高校基本科研业务费专项资金(DUT17LK58);国家自然科学基金(11672061)
详细信息
    通讯作者:

    朱强华

  • 中图分类号: TK124

A NOVEL FAST ALGORITHM BASED ON MODEL ORDER REDUCTION FOR ONE CLASS OF TRANSIENT NONLINEAR HEAT CONDUCTION PROBLEM

  • 摘要: 提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.

     

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出版历程
  • 收稿日期:  2019-11-19
  • 刊出日期:  2020-02-10

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