Semin, Adrien ; Schmidt, Kersten (2018)
On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model.
In: Proc. R. Soc. Lond. A, 474 (2210)
doi: 10.1098/rspa.2017.0708
Artikel, Bibliographie
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 |
| Art des Eintrags: | Bibliographie |
| Titel: | On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model |
| Sprache: | Englisch |
| Publikationsjahr: | Februar 2018 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Proc. R. Soc. Lond. A |
| Jahrgang/Volume einer Zeitschrift: | 474 |
| (Heft-)Nummer: | 2210 |
| DOI: | 10.1098/rspa.2017.0708 |
| URL / URN: | 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. |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 14 Nov 2018 13:18 |
| Letzte Änderung: | 14 Nov 2018 13:20 |
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