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Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations.

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Title: Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations.
Authors: Monteghetti, Florian1 florian.monteghetti@onera.fr, Matignon, Denis2 denis.matignon@isae.fr, Piot, Estelle1 estelle.piot@onera.fr
Source: Journal of Computational Physics. Dec2018, Vol. 375, p393-426. 34p.
Subjects: Discretization methods, Boundary value problems, Time-domain analysis, Euler equations, Galerkin methods
Abstract: Highlights • Admissibility of impedance boundary conditions is rigorously defined. • TDIBCs are shown to be best enforced through the scattering operator. • Validation of the analysis in a nonlinear impedance tube. • TDIBCs are deduced from the oscillatory-diffusive representation of physical models. • Application to two linear flow ducts. Abstract Time-domain impedance boundary conditions (TDIBCs) can be enforced using the impedance, the admittance, or the scattering operator. This article demonstrates the computational advantage of the last, even for nonlinear TDIBCs, with the linearized Euler equations. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow ducts. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 133047346
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  Label: Title
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  Data: Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations.
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  Data: <searchLink fieldCode="AR" term="%22Monteghetti%2C+Florian%22">Monteghetti, Florian</searchLink><relatesTo>1</relatesTo><i> florian.monteghetti@onera.fr</i><br /><searchLink fieldCode="AR" term="%22Matignon%2C+Denis%22">Matignon, Denis</searchLink><relatesTo>2</relatesTo><i> denis.matignon@isae.fr</i><br /><searchLink fieldCode="AR" term="%22Piot%2C+Estelle%22">Piot, Estelle</searchLink><relatesTo>1</relatesTo><i> estelle.piot@onera.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Dec2018, Vol. 375, p393-426. 34p.
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  Data: <searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Time-domain+analysis%22">Time-domain analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Euler+equations%22">Euler equations</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Highlights • Admissibility of impedance boundary conditions is rigorously defined. • TDIBCs are shown to be best enforced through the scattering operator. • Validation of the analysis in a nonlinear impedance tube. • TDIBCs are deduced from the oscillatory-diffusive representation of physical models. • Application to two linear flow ducts. Abstract Time-domain impedance boundary conditions (TDIBCs) can be enforced using the impedance, the admittance, or the scattering operator. This article demonstrates the computational advantage of the last, even for nonlinear TDIBCs, with the linearized Euler equations. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow ducts. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.jcp.2018.08.037
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 34
        StartPage: 393
    Subjects:
      – SubjectFull: Discretization methods
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Time-domain analysis
        Type: general
      – SubjectFull: Euler equations
        Type: general
      – SubjectFull: Galerkin methods
        Type: general
    Titles:
      – TitleFull: Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations.
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            NameFull: Monteghetti, Florian
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            NameFull: Matignon, Denis
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            NameFull: Piot, Estelle
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            – D: 15
              M: 12
              Text: Dec2018
              Type: published
              Y: 2018
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              Value: 375
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            – TitleFull: Journal of Computational Physics
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