Filter Based Stabilization Methods for Reduced Order Models of Convection-Dominated Systems
| dc.contributor.author | Moore, Ian Robert | en |
| dc.contributor.committeechair | Iliescu, Traian | en |
| dc.contributor.committeemember | Liu, Honghu | en |
| dc.contributor.committeemember | Zietsman, Lizette | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2023-05-16T08:01:48Z | en |
| dc.date.available | 2023-05-16T08:01:48Z | en |
| dc.date.issued | 2023-05-15 | en |
| dc.description.abstract | 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. | en |
| dc.description.abstractgeneral | Numerical 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.degree | Master of Science | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:36943 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/115065 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | Creative Commons Attribution-NonCommercial 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/4.0/ | en |
| dc.subject | Differential Filter | en |
| dc.subject | Reduced Order Model | en |
| dc.subject | Leray Model | en |
| dc.subject | Evolve-Filter-Relax | en |
| dc.subject | Approximate Deconvolution | en |
| dc.title | Filter Based Stabilization Methods for Reduced Order Models of Convection-Dominated Systems | en |
| dc.type | Thesis | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | masters | en |
| thesis.degree.name | Master of Science | en |