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dc.contributor.authorKoc, Birgul
dc.date.accessioned2019-02-08T14:16:37Z
dc.date.available2019-02-08T14:16:37Z
dc.date.issued2018-10-01
dc.identifier.urihttp://hdl.handle.net/10919/87537
dc.description.abstractWe investigate the effect of spatial filtering on the recently proposed data-driven correction reduced order model (DDC-ROM). We compare two filters: the ROM projection, which was originally used to develop the DDC-ROM, and the ROM differential filter, which uses a Helmholtz operator to attenuate the small scales in the input signal. We focus on the following questions: ``Do filtering and differentiation with respect to space variable commute, when filtering is applied to the diffusion term?'' or in other words ``Do we have commutation error (CE) in the diffusion term?" and ``If so, is the commutation error data-driven correction ROM (CE-DDC-ROM) more accurate than the original DDC-ROM?'' If the CE exists, the DDC-ROM has two different correction terms: one comes from the diffusion term and the other from the nonlinear convection term. We investigate the DDC-ROM and the CE-DDC-ROM equipped with the two ROM spatial filters in the numerical simulation of the Burgers equation with different diffusion coefficients and two different initial conditions (smooth and non-smooth).en_US
dc.format.mediumETDen_US
dc.language.isoen_USen_US
dc.publisherVirginia Techen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectReduced Order Modelingen_US
dc.subjectData-Driven Modeling
dc.subjectFiltering
dc.subjectClosure Modeling
dc.subjectCommutation Error
dc.titleCommutation Error in Reduced Order Modelingen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeM.S.en_US
thesis.degree.nameM.S.en_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairIliescu, Traian
dc.contributor.committeememberBorggaard, Jeffrey T.
dc.contributor.committeememberGugercin, Serkan
dc.description.abstractgeneralWe propose reduced order models (ROMs) for an efficient and relatively accurate numerical simulation of nonlinear systems. We use the ROM projection and the ROM differential filters to construct a novel data-driven correction ROM (DDC-ROM). We show that the ROM spatial filtering and differentiation do not commute for the diffusion operator. Furthermore, we show that the resulting commutation error has an important effect on the ROM, especially for low viscosity values. As a mathematical model for our numerical study, we use the one-dimensional Burgers equations with smooth and non-smooth initial conditions.en_US


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