用切比雪夫谱元方法求解均匀流场中的声传播问题

张荣欣; 秦国良

您当前的位置：

首页 >

文章列表页 >

用切比雪夫谱元方法求解均匀流场中的声传播问题

更新时间：2025-07-09

- 用切比雪夫谱元方法求解均匀流场中的声传播问题
- Chebychev Spectral Elements Method for Acoustic Propagation Problem in a Uniform Mean Flow
- 西安交通大学学报 2009年43卷第7期页码：120-124
- 作者机构：
  
  西安交通大学流体机械研究所,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  中图分类号： O42
- 网络首发：2009-07-10，
  
  纸质出版：2009
- 稿件说明：
移动端阅览
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.

Chebychev Spectral Elements Method for Acoustic Propagation Problem in a Uniform Mean Flow[J]. 2009, 43(7): 120-124.
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. DOI：

Chebychev Spectral Elements Method for Acoustic Propagation Problem in a Uniform Mean Flow[J]. 2009, 43(7): 120-124. DOI：

摘要

利用谱元方法中的无穷光滑插值函数的高阶精度特点

结合隐式时间推进算法的稳定性

推导并实现了低马赫数均匀流场中声波动方程的切比雪夫谱元解法

进而得到了流场影响下的声传播问题的数值解.该解法对均匀流场中的声传播问题在空间上进行谱元离散

在边界上引入Clayton-Engquist-Majda吸收边界条件

在时间上利用隐式Newmark积分方法推进求解.算例与解析解的对比验证表明:该解法在空间上可以实现高阶精度

在时间上达到2阶精度; 使用的隐式Newmark时间积分方法稳定性好

计算工作量相对较小; 当数值解达到稳态传播时和解析解吻合得非常好.随着计算条件的飞速发展

加密网格并采用更高阶的切比雪夫谱逼近可以进一步提高精度

以适应计算气动声学的精度要求

另外可尝试采用更高精度的吸收边界条件以改善边界反射对计算声场的干扰.

Abstract

High order accuracy is of great significance for computational aero-acoustics(CAA). On the basis of the high order accuracy of the infinite smooth interpolation function adopted in the spectral elements method

a Chebychev spectral elements approximation for the acoustic propagation problem in the subsonic uniform mean flow is applied in this study. In this approach

the discretization is based on spectral elements in space with first-order Clayton-Engquist-Majda absorbing boundary conditions and the implicit Newmark method in time marching. The numerical results with sixth-order spectral accuracy in space and up to second-order in time agree well with the analytical solutions. The Newmark method in time with less computing resource consumption also has the advantages of stability. The higher order spectral approximation can be employed to further enhance the accuracy and higher order absorbing boundary conditions might be applied to improve the spectral element approach.

关键词

Keywords

references

LIGHTHILL M J. On sound generated aerodynamically: general theory[J]. Proc Roy London Soc:Mathematical and Physical Science: 1952, 211(1107): 564-587.

LELE S K. Compact finite difference schemes with spectral like resolution[J]. Journal of Computational Physics, 1992, 103(1): 16-42.

JAE W K, DUCK J L. Optimized compact finite difference schemes with maximum resolution[J]. AIAA Journal, 1996, 34(5): 887-893.

傅德薰,马延文.高精度差分格式及多尺度流场特性的数值模拟[J].航空动力学报,2003,18(1):24-35.

FU Dexun, MA Yanwen. High order accurate schemes and numerical simulation of multi scale structures in complex flow fields [J]. Journal of Aerospace Power, 2003, 18(1): 24-35.

WU S W, LIAN S H, HSU L H. A finite element model for acoustic radiation[J]. Journal of Sound and Vibration, 1998, 215(3): 489-498.

HARTEN A, ENGQUIST A, OSHER S, et al. Uniformly high-order accuracy essentially non-oscillatory schemes:III[J]. Journal of Computational Physics, 1987, 71(2): 231-323.

TAM C K W, WEBB J C. Dispersion-relation-preserving finite difference schemes for computational acoustics[J]. Journal of Computational Physics, 1993, 107(2): 262-281.

TAM C K W. Computational aeroacoustics: issues and methods[J]. AIAA Journal, 1995, 33(10): 1788-1796.

LELE S K. Computational aeroacoustics: a review[C/OL]. Aerospace Science Meeting and Exhibit.[2008-09-05].http:∥www.aiaa.org/content.cfm?pageld.

PATERA A T. A spectral element method for fluid dynamics: laminar flow in a channel expansion[J]. Journal of Computational Physics, 1984, 54(3):468-488.

孙晓峰,周盛.气动声学[M].北京:国防工业出版社,1992:135-137.

CLAYTON R, ENGQUIST B. Absorbing boundary conditions for acoustic and elastic wave equations[J]. Bull Seism Soc Am, 1977, 67(6): 1527-1540.

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

许靖,秦国良,朱昌允.谱元方法求解含有吸收边界的声学问题[J].西安交通大学学报,2007,41(7): 875-878.

XU Jing, QIN Guoliang, ZHU Changyun.Chebychev spectral elements method for wave equation with absorbing boundary conditions[J]. Journal of Xi'an Jiaotong University, 2007, 41(7): 875-878.

王勖成. 有限单元法[M]. 北京:清华大学出版社, 2000:476-495.

邱志伟.谱元方法求解基于二阶吸收边界条件的气动声学问题[D].西安:西安交通大学能源与动力工程学院,2007.

离心风机气动噪声的数值预测.西安交通大学学报,2009,43(3):65-69

改变蜗壳宽度对离心风机气动噪声影响的数值计算与试验研究.2008,42(11):1429-1434.

一般相关噪声下线性系统定区间平滑估计算法.西安交通大学学报,2008,42(8):954-957.

谱元方法求解含吸收边界的声学问题.西安交通大学学报,2007,41(7):875-878.

谱无方法求解波动方程及影响其数值精度的相关因素.西安交通大学学报,2008,42(1):56-59.

前向离心风机吸声蜗壳降噪的试验研究.西安交通大学学报,2009,43(3):92-96.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

谱元法应用于涡声传播问题的研究

谱元方法求解含吸收边界的声学问题

Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播

面向高海拔空冷发电机防晕性能演化规律的电热耦合研究

混合电解槽阵列协同的风光耦合制氢系统双层多目标优化