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Seminar by Ping-Hsuan Tsai
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    :bdg-primary-line:`Speaker`

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        Ping-Hsuan Tsai (University of Illinois at Urbana-Champaign)

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        A Time-Relaxation Reduced Order Model for the Turbulent Channel Flow

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        * February 20, 2024 16:00 CET+0100 (Europe/Rome)
        * February 20, 2024 10:00 EST-0500 (US/Eastern)
        * February 20, 2024 09:00 CST-0600 (US/Central)
        * February 20, 2024 07:00 PST-0800 (US/Pacific)

    :bdg-primary-line:`Abstract`

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        Regularized reduced order models (Reg-ROMs) are stabilization strategies
        that leverage spatial filtering to alleviate the spurious numerical
        oscillations generally displayed by the classical Galerkin ROM (G-ROM)
        in under-resolved numerical simulations of turbulent flows. In this
        paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which
        filters the marginally resolved scales. We compare the new TR-ROM with
        the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and
        the evolve-filter-relax ROM (EFR-ROM), in the numerical simulation of
        the turbulent channel flow at :math:`Re_{\tau} = 180` and
        :math:`Re_{\tau} =
        395` in both the reproduction and the predictive regimes. For each
        Reg-ROM, we investigate two different filters:
        
        -  the differential filter (DF), and
        
        -  a new higher-order algebraic filter (HOAF).
        
        In our numerical investigation, we monitor the Reg-ROM performance with
        respect to the ROM dimension, :math:`N`, and the filter order. We also
        perform sensitivity studies of the three Reg-ROMs with respect to the
        time interval, relaxation parameter, and filter radius. The numerical
        results yield the following conclusions:
        
        -  In terms of the Reynolds normal and shear stresses, all three
           Reg-ROMs are significantly more accurate than the G-ROM.
        
        -  In addition, all three Reg-ROMs are more accurate than the ROM
           projection, which represents the best theoretical approximation of
           the training data in the given ROM space.
        
        -  With the optimal parameter values, the new TR-ROM yields more
           accurate results than the L-ROM and the EFR-ROM in all tests.
        
        -  For most :math:`N` values, DF yields the most accurate results for
           all three Reg-ROMs.
        
        -  The optimal parameters trained in the reproduction regime are also
           optimal for the predictive regime for most :math:`N` values,
           demonstrating the Reg-ROM predictive capabilities.
        
        -  All three Reg-ROMs are sensitive to the filter radius and the filter
           order, and the EFR-ROM and the TR-ROM are sensitive to the relaxation
           parameter.
        
        -  The optimal range for the filter radius and the effect of relaxation
           parameter are similar for the two :math:`Re_\tau` values.
        
        This is joint work with Paul Fischer and Traian Iliescu.

    :bdg-primary-line:`Recording`

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        Watch the recording on `our YouTube channel <https://www.youtube.com/watch?v=87_ADthgiO0>`_.