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

In 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2023

Author dc:creator

• Moore, Ian Robert

Chair dc:contributor.committeechair

• Iliescu, Traian

Committee members dc:contributor.committeemember

• Liu, Honghu
• Zietsman, Lizette

• Differential Filter
• Reduced Order Model
• Leray Model
• Evolve-Filter-Relax
• Approximate Deconvolution

Statement dc:rights

• Creative Commons Attribution-NonCommercial 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc/4.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:36943

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/115065