Speaker
Description
Spatial filtering has been widely used in under-resolved simulations of convection-dominated flows and, more recently, as a stabilization strategy in reduced order models (ROMs). However, spatial filters have key unresolved issues, such as determining the best-suited filter for specific applications or choosing an appropriate value for the filter radius.
To address these challenges, we introduce a fundamentally different approach that replaces traditional spatial filters with a data-driven stabilization operator (StabOp). The proposed StabOp is designed to deliver accurate results for a specified resolution, quantity of interest, and stabilization strategy. Although the framework applies to both classical discretizations and ROMs, as well as to various filter-based stabilization or closure techniques, we focus on ROMs with Leray stabilization.
To construct the StabOp, we assume a model form (linear, quadratic, or nonlinear) and determine its coefficients by solving a PDE-constrained optimization problem that minimizes a prescribed loss function. In the nonlinear case, the model is represented using a neural network, allowing for greater flexibility in capturing complex flow dynamics. Incorporating the learned operator into the Leray ROM (L-ROM) yields a new stabilized model, termed StabOp-L-ROM.
We evaluate the StabOp-L-ROM against the standard ROM and the classical L-ROM across four benchmark problems: 2D flow past a cylinder at Re = 500, lid-driven cavity flow at Re = 10000, 3D flow past a hemisphere at Re = 2200, and minimal channel flow at Re = 5000. The results demonstrate that, in predictive regimes, the StabOp-L-ROM can achieve accuracy improvements of several orders of magnitude over an optimally tuned L-ROM.