Chebychev Spectral Elements Method for Wave Equation with Absorbing Boundary Conditions

许靖; 秦国良; 朱昌允

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Chebychev Spectral Elements Method for Wave Equation with Absorbing Boundary Conditions

更新时间：2025-12-08

- Chebychev Spectral Elements Method for Wave Equation with Absorbing Boundary Conditions
- Vol. 41, Issue 7, Pages: 875-878(2007)
- 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：
  CLC： O42
- Online First：10 July 2007，
  
  Published：2007
- 稿件说明：
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许靖, 秦国良, 朱昌允. Chebychev Spectral Elements Method for Wave Equation with Absorbing Boundary Conditions[J]. 2007, 41(7): 875-878.
DOI：

许靖, 秦国良, 朱昌允. Chebychev Spectral Elements Method for Wave Equation with Absorbing Boundary Conditions[J]. 2007, 41(7): 875-878. DOI：

摘要

推导并实现了带吸收边界条件的二维波动方程的切比雪夫谱元解法.该解法引入一阶Clayton-Engquist-Majda吸收边界条件

在空间上利用谱元方法

在时间上利用中心差分的积分方法得到波动方程的离散形式

并给出具体算例进行了验证.结果表明:该解法在空间上具有谱精度

在时间上达到二阶精度; 与第一类边界条件相比

吸收边界有效地削弱了边界上的数值反射

避免了解的失真; 使用中心差分的时间积分方法同隐式积分方法相比

适合波的传播特性

避免了矩阵求逆运算

并且占用的计算机内存小.

Abstract

A Chebychev spectral elements approximation of the acoustic wave equation with first-order Clayton-Engquist-Majda absorbing boundary conditions was derived. Its discretization is based on spectral elements in space and central differences method in time. The numerical result

shows that this approximation has spectral accuracy in space and up to second-order in time. Compared with the same wave problems with conventional Dirichlet boundary conditions

the absorbing boundary conditions can reduce the numerical reflection on boundaries and avoid solution distortion. In addition

the central differences method is economic in memory requirement and computing time compared with implicit integral method.

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references

Alford R M, Kelly K R, Boore D M. Accuracy of finite-difference modeling of the acoustic wave equation[J].Geophysics,1974,39(4): 834-842.

Hughes T J R. The finite element method: linear static and dynamic finite element analysis[M]. New York, USA: Dover Publications Inc., 2000.

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.

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.

Renaut R, Froehlich J. Pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions[J]. Journal of Computational Physics, 1996,124:324-336.

邵秀民,刘臻. 带吸收边界条件的声波方程显示差分格式的稳定性分析[J]. 计算数学,2001,23(2):163-186.

Shao Xiumin, Liu Zhen.Stability analysis of explicit finite difference schemes for the acoustic wave equation with absorbing boundary conditions[J]. Mathematica Numerica Sinica, 2001, 23(2):163-186.

王勖成. 有限单元法[M]. 北京:清华大学出版社, 2000:491.

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