Show simple item record

dc.contributor.authorXie, X.en
dc.contributor.authorMohebujjaman, M.en
dc.contributor.authorRebholz, L. G.en
dc.contributor.authorIliescu, T.en
dc.date.accessioned2018-01-03T03:51:17Zen
dc.date.available2018-01-03T03:51:17Zen
dc.identifier.urihttp://hdl.handle.net/10919/81477en
dc.description.abstractWe propose a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows. The novel DDF-ROM framework consists of two steps: (i) In the first step, we use explicit ROM spatial filtering of the nonlinear PDE to construct a filtered ROM. This filtered ROM is low-dimensional, but is not closed (because of the nonlinearity in the given PDE). (ii) In the second step, we use data-driven modeling to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes. To this end, we use a quadratic ansatz to model this interaction and close the filtered ROM. To find the new coefficients in the closed filtered ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz. We emphasize that the new DDF-ROM is built on general ideas of spatial filtering and optimization and is independent of (restrictive) phenomenological arguments. We investigate the DDF-ROM in the numerical simulation of a 2D channel flow past a circular cylinder at Reynolds number $Re=100$. The DDF-ROM is significantly more accurate than the standard projection ROM. Furthermore, the computational costs of the DDF-ROM and the standard projection ROM are similar, both costs being orders of magnitude lower than the computational cost of the full order model. We also compare the new DDF-ROM with modern ROM closure models in the numerical simulation of the 1D Burgers equation. The DDF-ROM is more accurate and significantly more efficient than these ROM closure models.en
dc.relation.urihttp://arxiv.org/abs/1709.04362v1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectphysics.flu-dynen
dc.subjectphysics.flu-dynen
dc.titleData-Driven Filtered Reduced Order Modeling Of Fluid Flowsen
dc.typeArticle - Refereeden
dc.contributor.departmentMathematicsen
dc.description.notesarXiv admin note: substantial text overlap with arXiv:1702.06886en
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Mathematicsen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record