[1]沈淑君.数值求解纳米尺度热传导分数阶抛物两步模型[J].华侨大学学报(自然科学版),2023,44(1):133-140.[doi:10.11830/ISSN.1000-5013.202107037]
　SHEN Shujun.Numerical Solution for Nanoscale Heat Conduction Fractional Parabolic Two-Step Model[J].Journal of Huaqiao University(Natural Science),2023,44(1):133-140.[doi:10.11830/ISSN.1000-5013.202107037]
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数值求解纳米尺度热传导分数阶抛物两步模型()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第44卷
期数:
2023年第1期
页码:
133-140
栏目:
出版日期:
2023-01-10

文章信息/Info

Title:
Numerical Solution for Nanoscale Heat Conduction Fractional Parabolic Two-Step Model
文章编号:
1000-5013(2023)01-0133-08
作者:
沈淑君1; 2
1. 华侨大学 数学科学学院, 福建 泉州 362021;2. 华侨大学 计算科学福建省高校重点实验室, 福建 泉州 362021
Author(s):
SHEN Shujun1; 2
1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China; 2. Fujian Province University Key Laboratory of Computational Science, Huaqiao University, Quanzhou 362021, China
关键词:
纳米尺度热传导;  Caputo-Hadamard分数阶导数;  Robin边界条件;  紧有限差分格式
Keywords:
nanoscale heat conduction;  Caputo-Hadamard fractional-order derivative;  Robin’s boundary condition;  compact finite difference scheme
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202107037
文献标志码:
A
摘要:
提出一个纳米尺度的分数阶抛物两步模型,得到金属纳米尺度热传导的精确数值格式.该模型是通过引入Caputo-Hadamard时间分数阶导数到抛物型两步能量输运方程中,并将其温度跃变边界条件耦合得到.数值格式基于空间四阶紧格式和Caputo-Hadamard时间分数阶导数的L1逼近格式而建立.通过2个算例验证模型和数值方法的准确性和适用性.
Abstract:
A nanoscale fractional parabolic two-step model is presented, and an accurate numerical scheme for nanoscale heat conduction in metals is obtained. The model is obtained by introducing Caputo-Hadamard fractional-order derivative in time to the original parabolic two-step energy transport, and then coupling them with temperature-jump boundary condition. The numerical scheme is developed based on the space fourth-order compact finite difference scheme and the L1 approximation for Caputo-Hadamard time fractional-order derivative. The accuracy and applicability of the new model and the numerical method are tested by two numerical examples.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2021-07-27
通信作者: 沈淑君(1977-),女,副教授,博士,主要从事微分方程数值解的研究.E-mail:shensj12@sina.com.
基金项目: 国家自然科学基金资助项目(11501224); 福建省自然科学基金资助项目(2020J01074); 福建省高校创新团队发展计划,泉州市高层次人才团队项目(2017ZT012)
更新日期/Last Update: 2023-01-20