SBP-SAT方法及其在波动领域的应用  

A SBP-SAT method for the numerical solution and its application in the wave motion

作　　者：杨在林[1,2] 孙铖 蒋关希曦[1] 杨勇 YANG Zailin;SUN Cheng;JIANG Guanxixi;YANG Yong(College of Aerospace and Civil Engineering,Harbin Engineering University,Harbin 150080,China;Key Laboratory of Advanced Material of Ship and Mechanics,Ministry of Indus-try and Information Technology,Harbin Engineering University,Harbin 150080,China)

机构地区：[1]哈尔滨工程大学航天与建筑工程学院,哈尔滨150080 [2]哈尔滨工程大学工业与信息化部先进船舶材料与力学重点实验室,哈尔滨150080

出　　处：《振动与冲击》2020年第12期150-157,共8页Journal of Vibration and Shock

基　　金：国家重点研发计划(2017YFC1500801)。

摘　　要：基于分部求和(Summation By Parts)方法和同时逼近项(Simultaneous Approximation Terms)技术建立的有限差分方法,具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少,论文对该方法的研究背景,方法发展过程进行了介绍并基于SBP-SAT方法和弹性波动理论,结合初边值条件,推导出曲线网格条件下的弹性波动SBP-SAT离散方程。最后,通过数值模拟实现地震波传播过程,介绍该方法在地震数值模拟领域中的应用价值和前景。Summation by parts with simultaneous approximation terms has a set of properties that leads to provable time stability and higher order spatial discretization of partial differential equations.The finite difference methods based on this theory can establish a scheme that has incomparable advantages for simulating geometric discontinuity or complex media.At present,there are few researches on SBP-SAT methods in China.Therefore,this paper reviews the history of SBP-SAT methods and their application to the numerical solution of partial differential equations.Then,the discrete equations of elastic wave under the curvilinear coordinates were derived.At last,combining initial value conditions and boundary conditions,a simple simulation for imitating seismic wave propagation was performed.The potential and the application value were present.

关 键 词：SBP算子 有限差分法 边界条件 SAT 高阶方法 能量法 稳定性 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3