A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

Gasperini, David; Beise, Hans-Peter; Schroeder, Udo; Antoine, Xavier; Geuzaine, Christophe

doi:10.1137/21m1432363

SIAM J. Sci. Comput.

2022

DOI: 10.1137/21m1432363

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A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

David Gasperini¹,

Hans-Peter Beise²,

Udo Schroeder³

et al.

Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des labor… Show more

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Amplitude modulation of acoustic waves in accelerating flows quantified using acoustic black and white hole analogues

Schenke,

Sewerin,

van Wachem

et al. 2023

The Journal of the Acoustical Society of America

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We investigate the amplitude modulation of acoustic waves in accelerating flows, a problem that is still not fully understood, but essential to many technical applications, ranging from medical imaging to acoustic remote sensing. The proposed modeling framework is based on a convective form of the Kuznetsov equation, which incorporates the background flow field and is solved numerically by a finite-difference method. Using acoustic black and white hole analogues as model systems, we identify a modulation of the wave amplitude which is shown to be driven by the divergence/convergence of the acoustic wave characteristics in an accelerating/decelerating flow, and which is distinct from the convective amplification accompanying an acoustic emitter moving at a constant velocity. To rationalize the observed amplitude modulation, a leading-order model is derived from first principles, leveraging a similarity of the wave characteristics and the wave amplitude with respect to a modified Helmholtz number. This leading-order model may serve as a basis for the numerical prediction and analysis of the behavior of acoustic waves in accelerating flows, by taking advantage of the notion that any accelerating flow field can be described locally as a virtual acoustic black or white hole.

show abstract

Amplitude modulation of acoustic waves in accelerating flows quantified using acoustic black and white hole analogues

Schenke,

Sewerin,

van Wachem

et al. 2023

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

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A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

Cited by 1 publication

References 35 publications

Amplitude modulation of acoustic waves in accelerating flows quantified using acoustic black and white hole analogues

Amplitude modulation of acoustic waves in accelerating flows quantified using acoustic black and white hole analogues

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