This was part of
Reduced-Order Modeling for Complex Engineering Problems
Parametric Model-Order-Reduction for Turbulent-Flow Applications
Paul Fischer, Argonne National Laboratory
Monday, February 3, 2025
Abstract: We present recent developments in parametric model-order-reduction (pMOR) for
buoyancy-driven flows in the open source Navier-Stokes code, Nek5000/RS. The
main idea behind pMOR is to leverage high-fidelity simulations (aka full-order
models, or FOMs) of turbulent thermal/fluid problems that run on DOE's
leading-edge supercomputers to build reduced-order models (ROMs) that can run
on a laptop. There are two essential elements to the approach. One is the
reproduction problem, in which we build a model that is capable of tracking the
time evolution of quantities of interest (QOIs) at a given point in parameter
space (e.g., thermal loading conditions) using a low-rank ordinary differential
equation that governs representative solution modes. The modes typically come
from a proper orthogonal decomposition of FOM solution snapshots but it is also
possible to consider augmenting this basis with higher wavenumber modes derived
from nonlinear interactions of the POD modes [1]. The second element of pMOR
is to run the ROM at different test points in the parametric domain in order to
track QOI dependencies without rerunning the FOM.
This talk will primarily explore successes and limitations in ROM reproduction
of turbulent flow examples. We illustrate cases where pMOR is viable and also
examples where it is unable to extend beyond the training space. To aid in
understanding the pMOR/ROM process and the fundamental fluid mechanics itself
we seek to identify and characterize differences between flows where pMOR
succeeds and those where it fails.
[1] Kento Kaneko and Paul Fischer. Augmented reduced order models for turbulence.
Front. Phys. 10:905392. doi: 10.3389/fphy.2022.905392 (2022).
Paul Fischer (UIUC)
Viral Shah (UIUC)
Nicholas Christensen (UIUC)
Kento Kaneko (M.I.T.)
Ping-Hsuan Tsai (Virginia Tech)