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首页> 外文期刊>International Journal of Heat and Mass Transfer >A localized collocation scheme with fundamental solutions for long-time anomalous heat conduction analysis in functionally graded materials
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A localized collocation scheme with fundamental solutions for long-time anomalous heat conduction analysis in functionally graded materials

机译：一种局部搭配方案，具有功能分级材料的长时间异常导热分析基本解决方案

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摘要

This paper makes the first attempt to develop a novel localized collocation scheme based on fundamental solutions for long-time anomalous heat conduction analysis in functionally graded materials. In the present numerical framework, the Laplace transformation and Fixed Talbot numerical inverse Laplace transformation are employed to deal with the time fractional derivative in anomalous time fractional heat conduction model. The localized collocation scheme based on fundamental solutions is applied to solve Laplace-transformed time-independent partial differential equations (PDEs), and the generalized reciprocity method (GRM) coupled with the derived problem-dependent generalized fundamental solution is proposed to deal with the inhomogeneous term in Laplace-transformed time-independent PDEs. Numerical tests demonstrate that the developed computational strategy can be considered as one of the competitive alternatives in the simulation of anomalous heat conduction behavior of functionally graded materials. Furthermore, the effect of time fractional derivative order on the behavior of anomalous heat conduction is numerically investigated.
机译：本文首次试图基于功能分级材料的长时间异常热传导分析的基本解决方案开发一种新型局部配积方案。在本数值框架中，采用拉普拉斯变换和固定的Talbot数值逆拉普拉斯变换来处理异常时间分数传热模型中的时间分数衍生物。基于基本解决方案的局部搭配方案应用于求解拉普拉斯变换的时间无关的部分微分方程（PDE），并提出了与推导的问题依赖性广义基本解决方案耦合的广义互易性方法（GRM），以处理不均匀的在拉普拉斯变换时间无关的PDE中的术语。数值测试表明，开发的计算策略可以被认为是模拟功能梯度材料的异常导热行为的竞争替代方案之一。此外，数值研究了时间分数衍生顺序对异常热传导行为的影响。

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  • 来源
    《International Journal of Heat and Mass Transfer》 |2021年第12期|121778.1-121778.10|共10页
  • 作者

    Qiang Xi; Zhuojia Fu; Timon Rabczuk; Deshun Yin;

  • 作者单位

    Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing 211100 China;

    Key Laboratory of Ministry of Education for Coastal Disaster and Protection Hohai University. Nanjing 210098 China Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing 211100 China Institute of Continuum Mechanics Leibniz University Hannover Hannover 30167 Germany;

    Institute of Structural Mechanics Bauhaus-University Weimar Weimar 99423 Germany;

    Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing 211100 China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Anomalous heat conduction; Functionally graded materials; Time fractional derivative; Localized method of fundamental solutions; Generalized reciprocity method;

    机译：异常的热传导;功能分级材料;时间分数衍生物;本地化的基本解决方法;广义互惠方法;

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