Moore, Ian Robert2023-05-162023-05-162023-05-15vt_gsexam:36943http://hdl.handle.net/10919/115065In 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.ETDenCreative Commons Attribution-NonCommercial 4.0 InternationalDifferential FilterReduced Order ModelLeray ModelEvolve-Filter-RelaxApproximate DeconvolutionThesis