Filter Based Stabilization Methods for Reduced Order Models of Convection-Dominated Systems

dc.contributor.authorMoore, Ian Roberten
dc.contributor.committeechairIliescu, Traianen
dc.contributor.committeememberLiu, Honghuen
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.departmentMathematicsen
dc.date.accessioned2023-05-16T08:01:48Zen
dc.date.available2023-05-16T08:01:48Zen
dc.date.issued2023-05-15en
dc.description.abstractIn this thesis, I examine filtering based stabilization methods to design new regularized reduced order models (ROMs) for under-resolved simulations of unsteady, nonlinear, convection-dominated systems. The new ROMs proposed are variable delta filtering applied to the evolve-filter-relax ROM (V-EFR ROM), variable delta filtering applied to the Leray ROM, and approximate deconvolution Leray ROM (ADL-ROM). They are tested in the numerical setting of Burgers equation, a nonlinear, time dependent problem with one spatial dimension. Regularization is considered for the low viscosity, convection dominated setting.en
dc.description.abstractgeneralNumerical solutions of partial differential equations may not be able to be efficiently computed in a way that fully captures the true behavior of the underlying model or differential equation, especially if significant changes in the solution to the differential equation occur over a very small spatial area. In this case, non-physical numerical artifacts may appear in the computed solution. We discuss methods of treating these calculations with a goal of improving the fidelity of numerical solutions with respect to the original model.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:36943en
dc.identifier.urihttp://hdl.handle.net/10919/115065en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsCreative Commons Attribution-NonCommercial 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/en
dc.subjectDifferential Filteren
dc.subjectReduced Order Modelen
dc.subjectLeray Modelen
dc.subjectEvolve-Filter-Relaxen
dc.subjectApproximate Deconvolutionen
dc.titleFilter Based Stabilization Methods for Reduced Order Models of Convection-Dominated Systemsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen
Files
Original bundle
Now showing 1 - 2 of 2
Loading...
Thumbnail Image
Name:
Moore_IR_T_2023.pdf
Size:
1.13 MB
Format:
Adobe Portable Document Format
Name:
Moore_IR_T_2023_support_1.docx
Size:
12.33 KB
Format:
Microsoft Word XML
Description:
Supporting documents
Collections