Abstract:
Spatial filters have played a central role in large eddy simulation for many decades and, more recently, in Reduced Order Model (ROM) stabilization for convection-dominated flows. Nevertheless, important open questions remain: In under-resolved regimes, which filter is most suitable for a given stabilization or closure model? Moreover, once a filter is selected, how should its parameters, such as the filter radius, be determined? Addressing these questions are essential for the reliable design and performance of filter-based stabilization or closure strategies. To answer these critical questions, a novel strategy is proposed that is fundamentally different from current filter-based stabilizations and closures: The traditional spatial filters are replaced with a novel data-driven Stabilization Operator (StabOp) that yields the most accurate results for a given resolution, quantity of interest, and stabilization strategy. Although the new StabOp could be used for both classical discretizations and ROMs, and for different types of filter-based stabilization or closure, for clarity, it is investigated for ROMs and the Leray ROM (L-ROM) stabilization. To build the new StabOp, its model form is first postulated to be a linear mapping, a quadratic mapping, or a nonlinear neural network mapping, and then a PDE-constrained optimization problem is solved to minimize the given loss function. Using the resulting StabOp in the given L-ROM yields a new stabilized ROM, StabOp-L-ROM. To assess the new StabOp-L-ROM, it is compared with the L-ROM and the standard ROM in the numerical simulation of four under-resolved, convection-dominated flows: 2D flow past a cylinder at Re=500, lid-driven cavity at Re=10000, 3D flow past a hemisphere at Re=2200, and minimal channel flow at Re=5000. The numerical results demonstrate that the new StabOp-L-ROM can be orders-of-magnitude more accurate than the classical L-ROM tuned with the optimal filter radius in the predictive regime. Furthermore, while the new StabOp smooths the input flow fields, its smoothing mechanism is entirely different from those of classical spatial filters.
Speaker’s Bio:
Dr. Traian Iliescu is a professor in the Department of Mathematics and a College of Science Faculty Fellow at Virginia Tech. He won the Society for Industrial and Applied Mathematics Student Paper Prize in 1999, received his Ph.D. in 2000 from the University of Pittsburgh, was the 2000-2001 Wilkinson Fellow at Argonne National Laboratory, and joined Virginia Tech in 2002. His research is focused on the numerical simulation and analysis of turbulent engineering and geophysical flows, with a special emphasis on data-driven Galerkin methods and reduced order models.
