Advances in equation-based and data-driven modeling of fluid flows
Understanding the physics of complex fluid flows and devising control strategies to modify their behavior is crucial in several engineering applications, including commercial and military flight, wind energy systems, automotive aerodynamics, biomedical devices, and more. In this talk, we discuss recent advances in the analysis, model reduction and control of fluid flows. In the first half, we introduce the so-called “harmonic resolvent analysis,” which is a novel operator-theoretic framework tailored for flows that exhibit time-periodic behavior. These flows are ubiquitous in nature and engineering, with examples in aerodynamics, biological fluid mechanics, turbomachinery, fluid-structure interaction and many other fields. The harmonic resolvent formulation provides insights into the flow physics by studying the spectral properties of the harmonic resolvent operator, which is a frequency-domain input-output operator obtained by linearizing the governing equations about a time-periodic base flow. The use of this framework for the purposes of analyzing and controlling fluid flows is demonstrated on several examples, including the flow in the wake of an airfoil, a turbulent separated boundary layer and an axisymmetric jet undergoing vortex pairing. In the second half, we discuss a new model reduction method called “NiTROM: Non-intrusive Trajectory-based optimization of Reduced-Order Models.” This method addresses the long-standing issue of computing oblique projection operators for model reduction without intrusively accessing the governing equations. In turn, this allows for the computation of non-intrusive models with superior forecasting capabilities along transient trajectories, which is critical for several engineering tasks including reduced-order control design. We demonstrate the performance of NiTROM on two examples: the complex Ginzburg-Landau equation and the incompressible flow inside a lid-driven cavity.
Bio: Alberto Padovan is an assistant professor in the Department of Mechanical and Industrial Engineering at New Jersey Institute of Technology. Alberto’s research interests lie at the intersection of fluid mechanics, dynamical systems, and control theory, with a focus on developing scalable equation-based and data-driven algorithms for flow modeling, analysis and control. Before his current appointment, Alberto was a postdoc in the aerospace engineering department at the University of Illinois Urbana-Champaign, where he was also affiliated with the Center for Hypersonics and Entry Systems Studies (CHESS). Before then, he obtained his Ph.D. from the mechanical and aerospace engineering department at Princeton University in September 2022.