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Vortragende Person/Vortragende Personen:
Prof. Dr. Traian Iliescu

On 20^th december 2022 at 15:15, Prof. Dr. Traian Iliescu from the Virgina Polytechnic Institute and State University will give a talk.

Over the past decade, several closure and stabilization strategies
have been developed to tackle the ROM inaccuracy in the
convection-dominated, under-resolved regime, i.e., when the number of
degrees of freedom is too small to capture the complex underlying
dynamics. In this talk, I will survey regularized reduced order
models (Reg-ROMs), which are simple, modular stabilizations that
employ ROM spatial filtering of various terms in the Navier-Stokes
equations (NSE) to alleviate the spurious numerical oscillations
generally produced by standard ROMs in the convection-dominated,
under-resolved regime. I will focus on two different types of Reg-ROM
strategies: (i) the evolve-filter-relax ROM (EFR-ROM), which first
filters an intermediate velocity approximation, and then relaxes it;
and (ii) the Leray-ROM (L-ROM), which filters the convective term in
the NSE. Throughout my talk, I will highlight the impact made by ROM
spatial filtering on the Reg-ROM development. Specifically, I will
talk about the two main types of ROM spatial filters: (i) the ROM
differential filter; and (ii) the ROM projection. I will also propose
two novel higher-order ROM differential filters and discuss the
numerical analysis associated with ROM filtering. An important role
played in ROM spatial filters and Reg-ROMs is the ROM lengthscale. In
my talk, I will put forth a novel ROM lengthscale, which is
constructed by leveraging energy balancing arguments. I emphasize
that this novel energy-based lengthscale is fundamentally different
from the standard ROM lengthscale introduced decades ago, which is
based on simple dimensional arguments. Finally, I will illustrate the
success achieved by ROM spatial filters and Reg-ROMs in under-resolved
numerical simulations of the flow past a cylinder and turbulent
channel flow.