数值求解纳米尺度热传导分数阶抛物两步模型  

Numerical Solution for Nanoscale Heat Conduction Fractional Parabolic Two-Step Model

作　　者：沈淑君[1,2] SHEN Shujun(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China;Fujian Province University Key Laboratory of Computational Science,Huaqiao University,Quanzhou 362021,China)

机构地区：[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

出　　处：《华侨大学学报（自然科学版）》2023年第1期133-140,共8页Journal of Huaqiao University(Natural Science)

基　　金：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)。

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.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.

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 

分 类 号：O241.8[理学—计算数学]