Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播

耿艳辉; 秦国良

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Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播

更新时间：2025-07-09

- Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播
- Chebyshev Spectral Elements Method for 2-Dimensional Acoustic Propagation Problem in a Uniform Mean Flow with Absorbing Boundary Condition
- 西安交通大学学报 2012年46卷第3期页码：100-106
- 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：
  
  : 2011-07-13. 作者简介: 耿艳辉(1985-),女,博士生;秦国良(通信作者),男,教授. 基金项目: 国家自然科学基金资助项目(51076123)
- DOI：
  中图分类号： O42
- 网络首发：2012-03-10，
  
  纸质出版：2012
- 稿件说明：
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耿艳辉, 秦国良. Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播[J]. 西安交通大学学报, 2012,46(3):100-106.

Chebyshev Spectral Elements Method for 2-Dimensional Acoustic Propagation Problem in a Uniform Mean Flow with Absorbing Boundary Condition[J]. 2012, 46(3): 100-106.
耿艳辉, 秦国良. Chebyshev谱元法求解含吸收边界的二维均匀稳定流场的声传播[J]. 西安交通大学学报, 2012,46(3):100-106. DOI：

Chebyshev Spectral Elements Method for 2-Dimensional Acoustic Propagation Problem in a Uniform Mean Flow with Absorbing Boundary Condition[J]. 2012, 46(3): 100-106. DOI：

摘要

从群速度的角度推导了包含均匀稳定来流的二维波动方程的1阶吸收边界条件

基于Chebyshev谱元法提出了二维均匀稳定来流波动方程的求解方法.在空间上采用谱元方法

在时间上采用隐式 Newmark 积分法

从而获得了波动方程的离散形式.经具体算例验证表明:与1阶 Clayton-Engquist-Majda 吸收边界条件相比

所推导的吸收边界条件能更有效地削弱边界上的数值反射

避免解的失真

求解方法在空间上具有谱精度

在时间上达到了2阶精度.

Abstract

In this study

the Chebyshev spectral elements approximation was applied to solve the acoustic propagation problem in the subsonic uniform mean flow. From the group velocity

the first-order Eliane-Dan-Thomas absorbing boundary condition was derived for the boundaries of the solution domain. In this approach

the discretization of the wave equation is based on the spectral elements in space and the implicit Newmark method in time marching. The numerical results with higher-order spectral accuracy in space and second-order accuracy in time agree well with the benchmarksolutions. Compared with the first-order Clayton-Engquist-Majda absorbing boundary condition for the same wave problem

the first-order Eliane-Dan-Thomas absorbing boundary condition proposed here can effectively reduce the numerical reflection on boundaries and avoid solution distortion.

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Keywords

references

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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.

朱昌允,秦国良,徐忠. 谱元方法求解波动方程时显式与隐式差分方法的比较 [J]. 西安交通大学学报, 2008, 42(9):1142-1145.

ZHU Changyun, QIN Guoliang, XU Zhong. Comparison of explicit central difference method and implicit Newmark method using Chebyshev spectral element method for wave equations [J]. Journal of Xi'an Jiaotong University, 2008, 42(9):1142-1145.

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