Potential of data-driven discovery of nonlinear wave equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F24%3A00378654" target="_blank" >RIV/68407700:21230/24:00378654 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Potential of data-driven discovery of nonlinear wave equations
Original language description
Data-driven partial differential equation discovery techniques have been growing in importance in recent years. This paper discusses its possible applications in the field of finite-amplitude sound propagation and the related phenomena (such as generation of higher harmonics and shock formation). Two cases are investigated, namely the propagation of pressure pulses as travelling waves and the interference of pressure pulses, the former leading to the Westervelt equation and the latter to the Kuznetsov equation. It is shown how representative wave equations can be extracted from data obtained by numerically solving the compressible Navier-Stokes equations (up to the third order smallness in entropy changes) and subsequently employing the sparsity promoting regression techniques. The resulting error of the equation coefficients is about 7% in the nonlinear terms. The limitations of this approach are discussed (e.g., the appropriate capturing of thermal and viscous loss terms).
Czech name
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Czech description
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Project
<a href="/en/project/GA22-33896S" target="_blank" >GA22-33896S: Advanced methods of sound and elastic wave field control: acoustic black holes, metamaterials and functionally graded materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 53rd International Congress and Exposition on Noise Control Engineering, Nantes, France, 25-29 August 2024
ISBN
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ISSN
0736-2935
e-ISSN
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Number of pages
5
Pages from-to
3079-3083
Publisher name
Institute of Noise Control Engineering of the USA
Place of publication
Washington, DC
Event location
Nantes
Event date
Aug 25, 2024
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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