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Asymptotic analysis for acoustics in viscous gases close to rigid walls

Schmidt, Kersten ; Thöns-Zueva, Anastasia ; Joly, Patrick :
Asymptotic analysis for acoustics in viscous gases close to rigid walls.
[Online-Edition: http://dx.doi.org/10.1142/S0218202514500080]
In: Math. Models Meth. Appl. Sci., 24 (9) S. 1823-1855.
[Artikel] , (2014)

Offizielle URL: http://dx.doi.org/10.1142/S0218202514500080

Kurzbeschreibung (Abstract)

We derive a complete asymptotic expansion for the singularly perturbed problem of acoustic wave propagation inside gases with small viscosity. This derivation is for the non-resonant case in smooth bounded domains in two dimensions. Close to rigid walls the tangential velocity exhibits a boundary layer of size where η is the dynamic viscosity. The asymptotic expansion, which is based on the technique of multiscale expansion is expressed in powers of and takes into account curvature effects. The terms of the velocity and pressure expansion are defined independently by partial differential equations, where the normal component of velocities or the normal derivative of the pressure, respectively, are prescribed on the boundary. The asymptotic expansion is rigorously justified with optimal error estimates.

Typ des Eintrags: Artikel
Erschienen: 2014
Autor(en): Schmidt, Kersten ; Thöns-Zueva, Anastasia ; Joly, Patrick
Titel: Asymptotic analysis for acoustics in viscous gases close to rigid walls
Sprache: Englisch
Kurzbeschreibung (Abstract):

We derive a complete asymptotic expansion for the singularly perturbed problem of acoustic wave propagation inside gases with small viscosity. This derivation is for the non-resonant case in smooth bounded domains in two dimensions. Close to rigid walls the tangential velocity exhibits a boundary layer of size where η is the dynamic viscosity. The asymptotic expansion, which is based on the technique of multiscale expansion is expressed in powers of and takes into account curvature effects. The terms of the velocity and pressure expansion are defined independently by partial differential equations, where the normal component of velocities or the normal derivative of the pressure, respectively, are prescribed on the boundary. The asymptotic expansion is rigorously justified with optimal error estimates.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: Math. Models Meth. Appl. Sci.
Band: 24
(Heft-)Nummer: 9
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:28
DOI: 10.1142/S0218202514500080
Offizielle URL: http://dx.doi.org/10.1142/S0218202514500080
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