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Seminar by Traian Iliescu
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    :bdg-primary-line:`Speaker`

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        Traian Iliescu (Virginia Tech)

    :bdg-primary-line:`Title`

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        Regularized Reduced Order Models (Reg-ROMs) for Turbulent Flows

    :bdg-primary-line:`Date`

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        * January 31, 2023 16:00 CET+0100 (Europe/Rome)
        * January 31, 2023 10:00 EST-0500 (US/Eastern)
        * January 31, 2023 09:00 CST-0600 (US/Central)
        * January 31, 2023 07:00 PST-0800 (US/Pacific)

    :bdg-primary-line:`Abstract`

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        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. 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.
        
        Throughout my talk, I will discuss numerical analysis results proved for
        the Reg-ROMs that we proposed, including fundamental properties, e.g.,
        stability, convergence, and parameter scalings. I will also present some
        of the challenges and open questions in the development of rigorous
        numerical analysis foundations for ROM closures and stabilizations.
        
        This talk should be accessible to a wide audience, including students
        and postdocs.

    :bdg-primary-line:`Recording`

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        Watch the recording on `our YouTube channel <https://www.youtube.com/watch?v=Ev02xbkg5P0>`_.