阻尼色散波的人工边界条件  

Artificial boundary conditions for damped dispersive waves

作　　者：黄良易 王贤明 HUANG Liangyi;WANG Xianming(Key Laboratory of Special Equipment Manufacturing and Advanced Processing Technology of Ministry of Education,Sound and Vibration Laboratory,Zhejiang University of Technology,Hangzhou 310014)

机构地区：[1]浙江工业大学特种装备制造与先进加工技术教育部重点实验室,杭州310014

出　　处：《高技术通讯》2023年第11期1192-1201,共10页Chinese High Technology Letters

基　　金：国家自然科学基金(11602220)资助项目。

摘　　要：本文设计阻尼色散波问题的数值人工边界条件。本文采用匹配边界条件方法,通过匹配阻尼色散波的特征频率-波数关系,构造了准确的局部人工边界条件。匹配边界条件方法利用人工边界附近原子位移、速度的线性组合形式构造人工边界条件,并通过匹配色散波频率-波数关系的方式确定其组合系数。本文以一维无限长阻尼单原子链为例,以频率而非波数作为自变量,建立了阻尼色散波的频率-复数波数关系式。通过匹配该色散关系构造的匹配边界条件能够有效处理不同波速、不同空间衰减率的阻尼波。反射系数分析和数值算例均验证了此人工边界条件的有效性。该人工边界条件形式紧凑、构造方便、计算量小、吸收高效,适用于晶体的分子动力学模拟及多尺度计算。In this paper,numerical artificial boundary conditions for the damped dispersive wave problems are designed.The matching boundary condition method is used to construct accurate local artificial boundary conditions by matching the characteristic frequency-wave number relationship of damped dispersive waves.The matching boundary conditions take a linear combination form of atomic displacement and velocity near the artificial boundary,and the combination coefficients are determined by matching the frequency-wave number relationship.In this work,a onedimensional infinitely long damped monoatomic chain is taken as an example,and the frequency-wave number relationship of damped dispersive waves is established with frequency rather than wave number as the independent variable.The proposed matching boundary conditions can effectively deal with damped waves with different wave speeds and different spatial attenuation rates.Both reflection coefficient analysis and numerical examples verify the validity of the artificial boundary conditions.Matching boundary conditions are compact in form,low cost in computation,and efficient in absorption,and can be applied to molecular dynamics simulation and multi-scale calculation of crystals.

关 键 词：阻尼色散波 人工边界条件 匹配边界条件 色散关系 反射系数 多尺度计算 

分 类 号：O341[理学—固体力学]