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On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model

Semin, Adrien and Schmidt, Kersten :
On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model.
[Online-Edition: http://rspa.royalsocietypublishing.org/content/474/2210/2017...]
In: Proc. R. Soc. Lond. A, 474 (2210)
[Article] , (2018)

Official URL: http://rspa.royalsocietypublishing.org/content/474/2210/2017...

Abstract

The direct numerical simulation of the acoustic wave propagation in multiperforated absorbers with hundreds or thousands of tiny openings would result in a huge number of basis functions to resolve the microstructure. One is, however, primarily interested in effective and so homogenized transmission and absorption properties and how they are influenced by microstructure and its endpoints. For this, we introduce the surface homogenization that asymptotically decomposes the solution in a macroscopic part, a boundary layer corrector close to the interface and a near-field part close to its ends. The effective transmission and absorption properties are expressed by transmission conditions for the macroscopic solution on an infinitely thin interface and corner conditions at its endpoints to ensure the correct singular behaviour, which are intrinsic to the microstructure. We study and give details on the computation of the effective parameters for an inviscid and a viscous model and show their dependence on geometrical properties of the microstructure for the example of Helmholtz equation. Numerical experiments indicate that with the obtained macroscopic solution representation one can achieve an high accuracy for low and high porosities as well as for viscous boundary conditions while using only a small number of basis functions.

Item Type: Article
Erschienen: 2018
Creators: Semin, Adrien and Schmidt, Kersten
Title: On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model
Language: English
Abstract:

The direct numerical simulation of the acoustic wave propagation in multiperforated absorbers with hundreds or thousands of tiny openings would result in a huge number of basis functions to resolve the microstructure. One is, however, primarily interested in effective and so homogenized transmission and absorption properties and how they are influenced by microstructure and its endpoints. For this, we introduce the surface homogenization that asymptotically decomposes the solution in a macroscopic part, a boundary layer corrector close to the interface and a near-field part close to its ends. The effective transmission and absorption properties are expressed by transmission conditions for the macroscopic solution on an infinitely thin interface and corner conditions at its endpoints to ensure the correct singular behaviour, which are intrinsic to the microstructure. We study and give details on the computation of the effective parameters for an inviscid and a viscous model and show their dependence on geometrical properties of the microstructure for the example of Helmholtz equation. Numerical experiments indicate that with the obtained macroscopic solution representation one can achieve an high accuracy for low and high porosities as well as for viscous boundary conditions while using only a small number of basis functions.

Journal or Publication Title: Proc. R. Soc. Lond. A
Volume: 474
Number: 2210
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 14 Nov 2018 13:18
DOI: 10.1098/rspa.2017.0708
Official URL: http://rspa.royalsocietypublishing.org/content/474/2210/2017...
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