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. / Master of Science / 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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/115065 |
| Date | 15 May 2023 |
| Creators | Moore, Ian Robert |
| Contributors | Mathematics, Iliescu, Traian, Liu, Honghu, Zietsman, Lizette |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/vnd.openxmlformats-officedocument.wordprocessingml.document |
| Rights | Creative Commons Attribution-NonCommercial 4.0 International, http://creativecommons.org/licenses/by-nc/4.0/ |
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