A Linearized Viscous, Compressible Flow-Plate Interaction with Non-dissipative Coupling

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dc.contributor.authorAvalos, George
dc.contributor.authorGeredeli, Pelin Guven
dc.contributor.authorWebster, Justin
dc.date.accessioned2018-09-13T19:50:55Z
dc.date.available2018-09-13T19:50:55Z
dc.date.issued2019-05-14
dc.description.abstractWe address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so the fluid PDE includes an ambient flow profile U . In contrast to model in [Avalos, Geredeli, Webster, 2017], we track the effect of this term at the flow-structure interface, yielding a velocity matching condition involving the material derivative of the structure; this destroys the dissipative nature of the coupling of the dynamics. We adopt here a Lumer-Phillips approach, with a view of associating fluid-structure solutions with a C₀ -semigroup {eᴬᵗ}ₜ≥₀ on a chosen finite energy space of data. Given this approach, the challenge becomes establishing the maximal dissipativity of an operator A , yielding the flow-structure dynamics.en_US
dc.description.sponsorshipThe authors would like to sincerely thank Earl Dowell for his insight and expertise in discussing fluid flow modeling and coupling conditions (3.5), as presented in Section 2 [25]. The authors would like to thank the National Science Foundation, and acknowledge their partial funding from NSF Grant DMS-1616425 (G. Avalos and Pelin G. Geredeli). Pelin G. Geredeli also would like to thank the University of Nebraska-Lincoln for the Edith T. Hitz Fellowshipen_US
dc.description.urihttps://www.sciencedirect.com/science/article/pii/S0022247X19303476en_US
dc.format.extent26 pagesen_US
dc.genrejournal articlesen_US
dc.genrepostprints
dc.identifierdoi:10.13016/M2BR8MK6B
dc.identifier.citationAvalos, George, Pelin G. Geredeli, and Justin T. Webster. “A Linearized Viscous, Compressible Flow-Plate Interaction with Non-Dissipative Coupling.” Journal of Mathematical Analysis and Applications 477, no. 1 (September 1, 2019): 334–56. https://doi.org/10.1016/j.jmaa.2019.04.034.
dc.identifier.urihttps://doi.org/10.1016/j.jmaa.2019.04.034
dc.identifier.urihttp://hdl.handle.net/11603/11297
dc.language.isoen_USen_US
dc.publisherElsevier
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Information Systems Department
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.rightsCC BY-NC-ND 4.0 DEED Attribution-NonCommercial-NoDerivs 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectfluid-structure interactionen_US
dc.subjectcompressible viscous fluiden_US
dc.subjectplate, well-posednessen_US
dc.subjectsemigroupen_US
dc.subjectUMBC High Performance Computing Facility (HPCF)en_US
dc.titleA Linearized Viscous, Compressible Flow-Plate Interaction with Non-dissipative Couplingen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-2443-3789

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