Seminar by Ping-Hsuan Tsai

Speaker

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

Title

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

Date

  • 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)

Abstract

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 \(Re_{\tau} = 180\) and \(Re_{\tau} = 395\) 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, \(N\), 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 \(N\) 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 \(N\) 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 \(Re_\tau\) values.

This is joint work with Paul Fischer and Traian Iliescu.

Recording

Watch the recording on our YouTube channel.