标量波传播问题的双互易精细积分法

doi:10.19596/j.cnki.1001-246x.8003

计算物理 ›› 2020, Vol. 37 ›› Issue (1): 26-36.DOI: 10.19596/j.cnki.1001-246x.8003

标量波传播问题的双互易精细积分法

周枫林^1,2, 王炜佳¹, 廖海洋¹, 李光¹

1. 湖南工业大学机械工程学院, 湖南株洲 412007;
2. 湖南大学机械与运载工程学院, 湖南长沙 410082

收稿日期:2018-11-12 修回日期:2018-12-26 出版日期:2020-01-25 发布日期:2020-01-25
通讯作者: 李光(1963-),男,博士,教授,研究方向为工程数值方法,E-mail:liguanguw@126.com
作者简介:周枫林(1986-),男,博士,副教授,研究方向为工程数值方法,E-mail:edwal0zhou@163.com
基金资助:
国家自然科学基金（11602082）及湖南省教育厅资助科研项目（19B145）及株洲市科技计划资助项目

A Time Domain Dual Reciprocity Precise Integration Method for Scalar Wave Propagation Problems

ZHOU Fenglin^1,2, WANG Weijia¹, LIAO Haiyang¹, LI Guang¹

1. College of Mechanical Engineering, Hunan University of Technology, Zhuzhou, Hunan 412007, China;
2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China

Received:2018-11-12 Revised:2018-12-26 Online:2020-01-25 Published:2020-01-25

摘要/Abstract

摘要： 为避免使用计算多种特征频率下的声场响应，采用双互易方法将边界积分方程中时间二次导数项的域积分转化为边界积分.首先，将计算场点配置在边界上并考虑边界条件，可以获得由内部节点上声压量线性表示的边界节点上的物理量；其次，将计算场点配置于域内离散节点上，将所得边界积分方程组中关于边界物理量用内部节点的声压量线性表示，获得关于声压量的二阶常微分方程组；第三，引入声压变化速度作为未知量，将二阶常微分方程组转化为一阶常微分方程组；最后，采用精细积分法精确求解常微分方程组.数值算例验证了双互易精细积分法的正确性和稳定性.

关键词: 标量波传播, 边界积分方程, 双互易方法, 精细积分

Abstract: To avoid computation of multi-frequencies pressure in solution of frequency method, a dual reciprocity method (DRM) is applied to convert domain integral, which is related to derivatives of pressure over time, in boundary integral equation into boundary integral. Firstly, field points are collocated at all boundary nodes. With boundary condition, boundary quantities at boundary nodes can be represented linearly by quantities at domain nodes, which are applied for radial basis function interpolation and are arbitrarily distributed in DRM. Secondly, field points are further collocated at domain nodes. A system of ordinary differential equations (ODEs) of the second order is obtained. Thirdly, variation rate of pressure was introduced as an unknown quantity to reduce order of resulted ODEs. Finally, a precise integration method is adopted to solved the first ordered ODEs. Numerical examples demonstrated validity and stability of the method.

Key words: scalar wave propagation, boundary integral equation, dual reciprocity method, precise integration method

中图分类号:

P631.4

周枫林, 王炜佳, 廖海洋, 李光. 标量波传播问题的双互易精细积分法[J]. 计算物理, 2020, 37(1): 26-36.

ZHOU Fenglin, WANG Weijia, LIAO Haiyang, LI Guang. A Time Domain Dual Reciprocity Precise Integration Method for Scalar Wave Propagation Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 26-36.

参考文献

[1] GIBSON W C. The method of moments in electromagnetics[M]. New York:Chapman & Hall/CRC Press, 2007.
[2] LIU Y J. Fast multipole boundary element method:Theory and applications in engineering[M]. Cambridge:Cambridge University Press, 2011.
[3] WU H, LIU Y, JIANG W. A low-frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems[J]. Engineering Analysis with Boundary Elements, 2013, 37(2):309-318.
[4] WU H, YE W, JIANG W. A collocation BEM for 3D acoustic problems based on a non-singular Burton-Miller formulation with linear continuous elements[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 332:191-216.
[5] COOX L, ATAK O, VANDEPITTE D, DESMET W. An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 316:186-208.
[6] 王现辉, 乔慧, 张小明, 等. 基于等几何分析的边界元法求解Helmholtz问题[J]. 计算物理, 2017, 34(1):61-66.
[7] 王现辉, 郑兴帅, 乔慧,等. 二维Helmholtz边界超奇异积分方程解析研究[J]. 计算物理, 2017, 34(6):666-672.
[8] ERGIN A A, SHANKER B, MICHIELSSEN E. Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm[J]. The Journal of the Acoustical Society of America, 2000, 107(3):1168-1178.
[9] CHEN W, LI J, FU Z. Singular boundary method using time-dependent fundamental solution for scalar wave equations[J]. Computational Mechanics, 2016, 58(5):717-730.
[10] 王道平, 张量, 沈晶, 等. 基于紧致差分格式的高效时域有限差分算法[J]. 计算物理, 2014, 31(1):91-95.
[11] WU H, YE W, JIANG W. Isogeometric finite element analysis of interior acoustic problems[J]. Applied Acoustics, 2015, 100:63-73.
[12] 付梅艳, 陈再高, 王玥, 等. 基于三角形单元的时域有限积分方法研究[J]. 微波学报, 2010, (s1):83-87.
[13] GIMPERLEIN H, STARK D. On a preconditioner for time domain boundary element methods[J]. Engineering Analysis with Boundary Elements, 2018, 96(11):109-114.
[14] ABREU A I, CARRER J A M, MANSUR W J. A step by step scheme in BEM formulation for scalar wave equation[J]. Engineering Analysis with Boundary Elements, 2003, 27(2):101-105.
[15] CARRER J A M, MANSUR W J. Time-domain BEM analysis for the 2D scalar wave equation:initial conditions contributions to space and time derivatives[J]. International Journal of Numerical Methods in Engineering. 1996, 39:2169-2188.
[16] MERAL G, TEZER-Sezgin M. DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations[J]. Engineering Analysis with Boundary Elements, 2010, 34:547-580.
[17] ZHOU F L, ZHANG J M, SHENG X M, LI G Y. A dual reciprocity boundary face method for 3D non-homogeneous elasticity problems[J]. Engineering Analysis with Boundary Elements, 2012, 36(9):1301-1310.
[18] TANAKA M, MATSUMOTO T, TAKAKUWA S. Dual reciprocity BEM for time-stepping approach to the transient heat conduction problem in nonlinear materials[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(37):4953-4961.
[19] 高强, 谭述君, 钟万勰. 精细积分方法综述[J]. 中国科学:技术科学, 2016, 46(12):1207-1218.
[20] 钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994, 34:131-136.
[21] 钟万勰. 暂态历程的精细计算方法[J]. 计算结构力学及其应用, 1995, 12:1-6.
[22] ZHONG W X, ZHU J P, ZHONG X X. On a new time integration method for solving time dependent partial differential equations[J]. Computer Methods in Applied Mechanics and Engineering, 1996, 130:163-178.
[23] FASSHAUER G E, ZHANG J G. On choosing "optimal" shape parameters for RBF approximation[J]. Numerical Algorithms, 2007, 45:345-368.
[24] 谭述君. 精细积分方法的改进及其在动力学与控制中的应用[D]. 大连:大连理工大学,2009.

标量波传播问题的双互易精细积分法

A Time Domain Dual Reciprocity Precise Integration Method for Scalar Wave Propagation Problems

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