Numerical Analysis of Evolve Filter Relax Reduced Order Models (ERF-ROMs)
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This talk focuses on the development of the numerical analysis behind regularized reduced order models (ROMs) for turbulent flow. Direct numerical simulations have long been understood to be computationally infeasible for day-to-day simulations in computational fluid dynamics. ROMs have been shown to provide an efficient low-dimensional model capable of providing fast and accurate simulations. In the case of under-resolved flows, which is generally the case for high Reynolds numbers i.e. turbulent flows, standard ROM accuracy tends to suffer. Regularization, which is based on spatial filtering, increases the ROM stability and accuracy with negligible computational overhead. In this talk, we consider the Evolve Filter Relax framework as it relates to implicit methods for the Navier Stokes Equations. We analyze the numerical diffusion introduced by the scheme, as well as stability and convergence. Several numerical simulations are presented to support the analysis.
