Time-Space Coupled Spectral Element Method for Acoustic Wave Propagation on a Rigid Cylinder

doi:10.7652/xjtuxb201707004

您当前的位置：

首页 >

文章列表页 >

Time-Space Coupled Spectral Element Method for Acoustic Wave Propagation on a Rigid Cylinder

更新时间：2025-07-09

- Time-Space Coupled Spectral Element Method for Acoustic Wave Propagation on a Rigid Cylinder
- Vol. 51, Issue 7, Pages: 24-29+97(2017)
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201707004
  CLC： O422
- Online First：10 July 2017，
  
  Published：2017
- 稿件说明：
移动端阅览
Time-Space Coupled Spectral Element Method for Acoustic Wave Propagation on a Rigid Cylinder[J]. 2017, 51(7): 24-29+97.
DOI：

Time-Space Coupled Spectral Element Method for Acoustic Wave Propagation on a Rigid Cylinder[J]. 2017, 51(7): 24-29+97. DOI： 10.7652/xjtuxb201707004.

摘要

以刚性圆柱体表面均匀分布若干单极子质量源的声传播问题为求解目标

在极坐标系中构建时空耦合模型。基于Least-Squares变分

在时间及空间方向同时采用Chebyshev谱元方法进行离散

将原来极坐标系中的问题转化到柱坐标系中进行求解

并通过数值实验验证了模型的正确性; 进一步应用时空耦合模型求解刚性圆柱体表面声传播问题

在计算区域外边界采用C-E-M吸收边界条件。研究结果显示:时空耦合谱元模型通过时间及空间计算精度的匹配

能够获得高精度的数值解; 增加时间及空间方向的单元数及单元内的插值阶数均能提高计算精度

且提高插值阶数的方法具有指数阶收敛特性; 所构建的时空耦合模型能够稳定求解刚性圆柱体表面的声传播问题

将C-E-M吸收边界条件改写为第一类边界条件并应用于时空耦合模型依然有效。研究内容对构建高精度的计算气动声学求解方法具有指导意义。

Abstract

A coupled time-space model is established in a polar coordinate to obtain the propagation characters from some monopole sources distributed evenly on a rigid cylinder. Following the least-squares variational principle

Chebyshev spectral element method is chosen to discretize both the time and space domains and the problem in polar coordinate is transformed into cylindrical coordinate. The validity of this model is verified by the numerical experiment

and the acoustic wave propagation on a rigid cylinder with C-E-M absorbing boundary condition on the edge of computational domain is revealed. The results show that a high-order accuracy can be obtained by the coupled time-space model via matching the numerical accuracy between time and space. The numerical accuracy can be improved by increasing the number of the elements or the interpolation order in each element of time and space. An exponential accuracy rate can be obtained with the increasing interpolation order. The acoustic wave propagation on the surface of a rigid cylinder can be simulated stably by this model

and the C-E-M absorbing boundary condition rewritten as the Dirichlet boundary condition still works well.

关键词

Keywords

references

SESCU A, HIXON R, AFJEH A A. Multidimensional optimization of finite difference schemes for computational aeroacoustics [J]. Journal of Computational Physics, 2008, 227(9): 4563-4588.

TREYSSÈDE F, GABARD G, TAHAR M B. A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description [J]. Journal of the Acoustical Society of America, 2003, 113(2): 705-716.

PATERA A T. A spectral element method for fluid dynamics-laminar flow in a channel expansion [J]. Journal of Computational Physics, 1984, 54: 468-488.

张荣欣, 秦国良. 用切比雪夫谱元方法求解均匀流场中的声传播问题 [J]. 西安交通大学学报, 2009, 43(7): 120-124.

ZHANG Rongxin, QIN Guoliang. Chebyshev spectral elements method for acoustic propagation problem in a uniform mean flow [J]. Journal of Xi'an Jiaotong University, 2009, 43(7): 120-124.

ZHU C, QIN G, ZHANG J. Implicit Chebyshev spectral element method for acoustics wave equations [J]. Finite Elements in Analysis and Design, 2011, 47(2): 184-194.

ZHANG R, QIN G, ZHU C. Spectral elements method for acoustic propagation problems based on linearized Euler equations [J]. Journal of Computational Acoustics, 2009, 17(4): 383-402.

GENG Yanhui, QIN Guoliang, WANG Yang, et al. The research of space-time coupled spectral element method for acoustics wave equations [J]. Chinese Journal of Acoustics. 2016, 35(1): 29-47.

LIN W H. Least-squares Legendre spectral element solutions to sound propagation problems [J]. Journal of the Acoustical Society of America, 2001, 109: 465-474.

王亚洲, 秦国良, 和文强, 等. 时空耦合谱元方法求解一维Burgers方程 [J]. 西安交通大学学报, 2017, 51(1): 45-50.

WANG Yazhou, QIN Guoliang, HE Wenqiang, et al. Time-space coupled spectral element method for one-dimensional Burgers equation [J]. Journal of Xi'an Jiaotong University, 2017, 51(1): 45-50.

CLAYTON R, ENGQUIST B. Absorbing boundary conditions for acoustic and elastic wave equations [J]. Bulletin of the Seismological Society of America, 1977, 67(6): 1529-1540.

ENGQUIST B, MAJDA A. Absorbing boundary conditions for the numerical simulation of waves [J]. Mathematics of Computation, 1977, 31(139): 629-651.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Least-Squares and Galerkin Spectral Element Methods for Poisson Equation in Annular Regions

Comparison of Explicit Central Difference Method and Implicit Newmark Method Using Chebyshev Spectral Element Method for Wave Equations

Implicit Spectral Element Method for Wave Equation and Some Factors Influencing Numerical Accuracy

Time-Space Coupled Spectral Element Method for One-Dimensional Burgers Equation

Research on the Electrohydrodynamic Effects of Ionic Liquid-Modified Fuels

Related Author

王亚洲

秦国良

朱昌允

秦国良

徐忠

王亚洲

秦国良

和文强

Related Institution

No data

⁰