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Time-domain implementation of an impedance boundary condition with boundary layer correction

Time-domain implementation of an impedance boundary condition with boundary layer correction
Time-domain implementation of an impedance boundary condition with boundary layer correction
A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.
0021-9991
755-775
Brambley, Ed J.
ae317fd1-bb34-419d-9d53-f9b9c38ee546
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Brambley, Ed J.
ae317fd1-bb34-419d-9d53-f9b9c38ee546
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7

Brambley, Ed J. and Gabard, Gwenael (2016) Time-domain implementation of an impedance boundary condition with boundary layer correction. Journal of Computational Physics, 321, 755-775. (doi:10.1016/j.jcp.2016.05.064).

Record type: Article

Abstract

A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

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Submitted date: 22 January 2016
Accepted/In Press date: 31 May 2016
e-pub ahead of print date: 8 June 2016
Published date: 15 September 2016
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 399368
URI: http://eprints.soton.ac.uk/id/eprint/399368
ISSN: 0021-9991
PURE UUID: 5c4a0977-9e85-4e3b-bc09-ee6576ec8881

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Date deposited: 15 Aug 2016 10:38
Last modified: 03 Dec 2019 06:36

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Contributors

Author: Ed J. Brambley
Author: Gwenael Gabard

University divisions

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