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

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Date
2023-05-15
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Virginia Tech
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.

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Keywords
Differential Filter, Reduced Order Model, Leray Model, Evolve-Filter-Relax, Approximate Deconvolution
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