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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 ; 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)
[Artikel] , (2018)

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

Kurzbeschreibung (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.

Typ des Eintrags: Artikel
Erschienen: 2018
Autor(en): Semin, Adrien ; Schmidt, Kersten
Titel: On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model
Sprache: Englisch
Kurzbeschreibung (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.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: Proc. R. Soc. Lond. A
Band: 474
(Heft-)Nummer: 2210
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 14 Nov 2018 13:18
DOI: 10.1098/rspa.2017.0708
Offizielle URL: http://rspa.royalsocietypublishing.org/content/474/2210/2017...
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