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An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations

Quero, David (2019) An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations. In: AIAA Aviation 2019 Forum. AIAA AVIATION Forum, 2019-06-17 - 2019-06-21, Dallas, TX (USA). doi: 10.2514/6.2019-3529. ISBN 978-162410589-0.

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Offizielle URL: https://arc.aiaa.org/doi/10.2514/6.2019-3529

Kurzfassung

In this work a novel approach in determining the first and second order frequencydomain Volterra kernels for weakly nonlinear partial differential equations (PDEs) in semidiscrete form based on the application of the harmonic probing (HP) method is presented. This represents a formal extension of the linearized-frequency domain (LFD) methods to a nonlinear framework, leading to a so-called LFD2 method. The method allows for the representation of weak nonlinearities by solving two input-independent linear algebraic systems of equations in the frequency domain and thus circumvents the solution of the nonlinear PDE by numerical integration for each different input, representing a nonlinear reduced-order model (ROM) for the physical phenomena. The general form of the equations is derived and an application to the well known viscous Burgers’ equation to show its suitability in representing the nonlinear convective term is shown. Next, an application to the compressible quasi one-dimensional unsteady flow described by the Euler equations is presented. The proposed method overcomes two constraints present in other methods for the solution of nonlinear PDEs, namely, the consideration of exclusively periodic solutions as in the harmonic balance (HB) method and the dependency of the kernels with the input signal as in the Volterra kernel identification methods.

elib-URL des Eintrags:https://elib.dlr.de/128080/
Dokumentart:Konferenzbeitrag (Vortrag)
Titel:An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations
Autoren:
AutorenInstitution oder E-Mail-AdresseAutoren-ORCID-iDORCID Put Code
Quero, DavidDavid.QueroMartin (at) dlr.deNICHT SPEZIFIZIERTNICHT SPEZIFIZIERT
Datum:2019
Erschienen in:AIAA Aviation 2019 Forum
Referierte Publikation:Ja
Open Access:Ja
Gold Open Access:Nein
In SCOPUS:Ja
In ISI Web of Science:Nein
DOI:10.2514/6.2019-3529
ISBN:978-162410589-0
Status:veröffentlicht
Stichwörter:linearized-frequency domain, Volterra kernels, nonlinear, reduced order model
Veranstaltungstitel:AIAA AVIATION Forum
Veranstaltungsort:Dallas, TX (USA)
Veranstaltungsart:internationale Konferenz
Veranstaltungsbeginn:17 Juni 2019
Veranstaltungsende:21 Juni 2019
Veranstalter :AIAA
HGF - Forschungsbereich:Luftfahrt, Raumfahrt und Verkehr
HGF - Programm:Luftfahrt
HGF - Programmthema:Flugzeuge
DLR - Schwerpunkt:Luftfahrt
DLR - Forschungsgebiet:L AR - Aircraft Research
DLR - Teilgebiet (Projekt, Vorhaben):L - Flugphysik (alt)
Standort: Göttingen
Institute & Einrichtungen:Institut für Aeroelastik > Aeroelastische Simulation
Hinterlegt von: Quero-Martin, David
Hinterlegt am:09 Jul 2019 09:24
Letzte Änderung:24 Apr 2024 20:31

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