有限差分法求解声子热输运方程  

FINITE DIFFERENCE METHOD FOR SIMULATING PHONON HEAT TRANSPORT PROCESS

作　　者：陈建灵 冯仰德[1] Chen Jianling;Feng Yangde(Computer Network Information Center, Department of High Performance Computing Technologyand Application Development, CAS, Beijing 100190, China;University of Chinese Academy of Sciences, Beijing 100049, China)

机构地区：[1]中国科学院计算机网络信息中心,高性能计算技术与应用发展部,北京100190 [2]中国科学院大学,北京100049

出　　处：《数值计算与计算机应用》2019年第3期215-229,共15页Journal on Numerical Methods and Computer Applications

基　　金：中国科学院科研信息化应用工程(XXH13506-407)

摘　　要：声子辐射输运方程是一个微分-积分方程,使用有限差分法数值求解具有边界条件的声子辐射输运方程,可借助Gauss-Seidel方法和有限差分离散化来保证得到稳定的数值解.通过对室温下Ge/Si/Ge薄膜的声子热输运过程进行一维数值模拟,以及对界面处使用漫射失配界面模型,可以得到温度沿着薄膜法向方向的变化曲线和Ge/Si薄膜厚度比例与温度在界面处跳跃值对材料整体结构的热导率的影响,以及随着薄膜厚度的增加薄膜热导率的变化趋势;对硅薄膜声子热输运过程进行二维数值模拟,可以得到温度沿着薄膜法向和面向方向的分布情况,以及当薄膜宽度和厚度比例不同时温度的变化和法向热导率的变化.The Equation of Phonon Radiative Transfer is a differential-integral equation.The finite difference method is used to numerically solve the Equation of Phonon Radiative Transfer with boundary conditions.The Gauss-Seidel method and the finite difference discretization can be used to ensure stable numerical solutions.Through one-dimensional numerical simulation of the phonon heat transport process of Ge/Si/Ge film at room temperature and by using the diffuse mismatch interface model at the interface,it can evaluate the influence of the temperature along the normal direction of the film and the thickness ratio of the Ge/Si film and the temperature jump at the interface on the thermal conductivity of the overal-1 structure of the material,and the change of the thermal conductivity of the film as the thickness of the film increases.The two-dimensional numerical simulation of the phonon heat transport process of the silicon film can obtain the temperature along the the normal and orientation-oriented distribution of the film,and the change in temperature and the thermal conductivity when the film width and thickness ratio are different.

关 键 词：声子辐射输运方程 有限差分法 离散化 温度 热导率 

分 类 号：O241.3[理学—计算数学]