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



Slides
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)