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Asymptotic analysis for acoustics in viscous gases close to rigid walls

Schmidt, Kersten and Thöns-Zueva, Anastasia and 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) pp. 1823-1855.
[Article] , (2014)

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

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.

Item Type: Article
Erschienen: 2014
Creators: Schmidt, Kersten and Thöns-Zueva, Anastasia and Joly, Patrick
Title: Asymptotic analysis for acoustics in viscous gases close to rigid walls
Language: English
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.

Journal or Publication Title: Math. Models Meth. Appl. Sci.
Volume: 24
Number: 9
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:28
DOI: 10.1142/S0218202514500080
Official URL: http://dx.doi.org/10.1142/S0218202514500080
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