Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents

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dc.contributor.authorXie, Xupingen
dc.contributor.authorNolan, Peter J.en
dc.contributor.authorRoss, Shane D.en
dc.contributor.authorMou, Changhongen
dc.contributor.authorIliescu, Traianen
dc.contributor.departmentBiomedical Engineering and Mechanicsen
dc.contributor.departmentAerospace and Ocean Engineeringen
dc.contributor.departmentMathematicsen
dc.date.accessioned2020-10-27T13:17:44Zen
dc.date.available2020-10-27T13:17:44Zen
dc.date.issued2020-10-23en
dc.date.updated2020-10-26T14:24:47Zen
dc.description.abstractThere are two main strategies for improving the projection-based reduced order model (ROM) accuracy&mdash;(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote <inline-formula><math display="inline"><semantics><mi>&alpha;</mi></semantics></math></inline-formula>-ROM and <inline-formula><math display="inline"><semantics><mi>&lambda;</mi></semantics></math></inline-formula>-ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the <inline-formula><math display="inline"><semantics><mi>&alpha;</mi></semantics></math></inline-formula>-ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs&rsquo; accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis.en
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationXie, X.; Nolan, P.J.; Ross , S.D.; Mou , C.; Iliescu, T. Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents. Fluids 2020, 5, 189.en
dc.identifier.doihttps://doi.org/10.3390/fluids5040189en
dc.identifier.urihttp://hdl.handle.net/10919/100716en
dc.language.isoenen
dc.publisherMDPIen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectLagrangian reduced order modelen
dc.subjectLagrangian inner producten
dc.subjectquasi-geostrophic equationsen
dc.subjectfinite time Lyapunov exponenten
dc.titleLagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponentsen
dc.title.serialFluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.dcmitypeStillImageen

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Journal Articles, Multidisciplinary Digital Publishing Institute (MDPI)
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