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Construction and Analysis of an Adapted Spectral Finite Element Method to Convective Acoustic Equations

Part of: Basic methods in fluid mechanics Partial differential equations, initial value and time-dependent initial-boundary value problems General aerodynamics and subsonic flows

Published online by Cambridge University Press:  22 June 2016

Andreas Hüppe ,
Gary Cohen ,
Sébastien Imperiale  and
Manfred Kaltenbacher
Andreas Hüppe*
Affiliation:
TU Wien, Institute of Mechanics and Mechatronics, Getreidemarkt 9/E325, 1060 Wien, Austria
Gary Cohen*
Affiliation:
Inria-CNRS-ENSTA, Saclay Ile-de-France, 91120 Palaiseau, France
Sébastien Imperiale*
Affiliation:
Inria, Saclay Ile-de-France, 91120 Palaiseau, France
Manfred Kaltenbacher*
Affiliation:
TU Wien, Institute of Mechanics and Mechatronics, Getreidemarkt 9/E325, 1060 Wien, Austria
*
*Corresponding author. Email addresses:andreas.hueppe@tuwien.ac.at (A. Hüppe), Gary.Cohen@ensta-paristech.fr (G. Cohen), sebastien.imperiale@inria.fr (S. Imperiale), manfred.kaltenbacher@tuwien.ac.at (M. Kaltenbacher)
*Corresponding author. Email addresses:andreas.hueppe@tuwien.ac.at (A. Hüppe), Gary.Cohen@ensta-paristech.fr (G. Cohen), sebastien.imperiale@inria.fr (S. Imperiale), manfred.kaltenbacher@tuwien.ac.at (M. Kaltenbacher)
*Corresponding author. Email addresses:andreas.hueppe@tuwien.ac.at (A. Hüppe), Gary.Cohen@ensta-paristech.fr (G. Cohen), sebastien.imperiale@inria.fr (S. Imperiale), manfred.kaltenbacher@tuwien.ac.at (M. Kaltenbacher)
*Corresponding author. Email addresses:andreas.hueppe@tuwien.ac.at (A. Hüppe), Gary.Cohen@ensta-paristech.fr (G. Cohen), sebastien.imperiale@inria.fr (S. Imperiale), manfred.kaltenbacher@tuwien.ac.at (M. Kaltenbacher)
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Abstract

The paper addresses the construction of a non spurious mixed spectral finite element (FE) method to problems in the field of computational aeroacoustics. Based on a computational scheme for the conservation equations of linear acoustics, the extension towards convected wave propagation is investigated. In aeroacoustic applications, the mean flow effects can have a significant impact on the generated sound field even for smaller Mach numbers. For those convective terms, the initial spectral FE discretization leads to non-physical, spurious solutions. Therefore, a regularization procedure is proposed and qualitatively investigated by means of discrete eigenvalues analysis of the discrete operator in space. A study of convergence and an application of the proposed scheme to simulate the flow induced sound generation in the process of human phonation underlines stability and validity.

Keywords

Spectral finite elementsaeroacousticsperturbation equations

MSC classification

Secondary: 76M10: Finite element methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76G25: General aerodynamics and subsonic flows
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 1 , July 2016 , pp. 1 - 22
Copyright
Copyright © Global-Science Press 2016 

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