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**Schmidt, Kersten and Thöns-Zueva, Anastasia and Joly, Patrick** (2014):

*Asymptotic analysis for acoustics in viscous gases close to rigid walls.*

In: Math. Models Meth. Appl. Sci., pp. 1823-1855, 24, (9), DOI: 10.1142/S0218202514500080, [Online-Edition: http://dx.doi.org/10.1142/S0218202514500080],

[Article]

## 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 Î· 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 Î· 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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