水下声波传播过程的时域间断Galerkin有限元方法  

A time discontinuous Galerkin finite element method for the propagation process of the acoustic wave in water

作　　者：李瑞敏 郭攀[1] 张景飞[1] 武文华[2] 王飞[1] LI Rui-min;GUO Pan;ZHANG Jing-fei;WU Wen-hua;WANG Fei(School of Mechanics and Safety Engineering,Zhengzhou University,Zhengzhou 450000,China;State Key Laboratory for Structural Analysis of Industrial Equipment,Department of Engineering Mechanics,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]郑州大学力学与安全工程学院,郑州450000 [2]大连理工大学运载工程与力学学部工程力学系,工业装备结构分析国家重点实验室,大连116024

出　　处：《计算力学学报》2021年第2期166-172,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学青年基金(51904272);河南省高等学校重点科研项目计划(18A620003);河南省博士后科研项目(00182001)资助项目.

摘　　要：本文构建了声压波动方程的改进时域间断Galerkin有限元方法。传统时域连续有限元方法在计算高梯度、强间断特征水中声波传播问题时往往会出现虚假数值振荡现象,这些数值振荡会影响正常波动的计算精度。为了解决这一问题,本文通过引入人工阻尼的方式构建了改进的时域间断Galerkin有限元方法,并针对具有高梯度、强间断特征的多障碍物复杂边界和层合液体介质声传播问题进行了计算。计算结果表明,与传统时域连续方法如Newmark方法计算结果对比,所发展方法能较好地消除高梯度和强间断声压力波传播过程中虚假的数值振荡,具有较高的计算精度。问题的求解为进一步流固声耦合问题的研究奠定了基础。In this paper,an improved time-domain discontinuous Galerkin finite element method for the acoustic wave equation is constructed.Traditional time-domain continuous finite element methods often produce spurious numerical oscillations when calculating acoustic wave propagation problems of high gradient and strongly discontinuous features.These numerical oscillations will affect the calculation accuracy of an simulation of acoustic wave.In order to solve this problem,this paper constructs an improved time-domain discontinuous Galerkin finite element method,and calculates the acoustic propagation problem of multi-obstacles with complex boundaries and laminated liquid media with high gradients and strong discontinuities.The results show that the developed method can better filter out the effects of spurious numerical oscillations during the propagation of high gradient and strong intermittent acoustic pressure waves,and have much more accurate solutions than the traditional time-domain continuous finite element method such as Newmark method.This method can also be used to the further calculation of fluid-structure-acoustic coupling under shock conditions.

关 键 词：声波 时域间断伽辽金有限元方法 冲击 数值振荡 

分 类 号：P733.21[天文地球—物理海洋学] O242.21[天文地球—海洋科学]