2023/11/10 by Alireza Amiri-Margavi, Hessam Babaee, Amiri-Margavi, Alireza +1 · 1 citation
Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Model Reduction and Neural Networks #Structural Health Monitoring Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2312.00790
openalex publication_date 2023/11/10 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
Understanding the linear growth of disturbances due to external forcing is crucial for flow stability analysis, flow control, and uncertainty quantification. These applications typically require a large number of forward simulations of the forced linearized dynamics, often in a brute-force fashion. When dealing with simple steady-state or periodic base flows, there exist powerful and cost-effective solution operator techniques. Once these solution operators are constructed, they can be used to determine the response to various forcings with negligible computational cost. However, these methods do not apply to problems with arbitrarily time-dependent base flows. This paper develops and investigates reduced-order modeling with time-dependent bases (TDBs) to build low-rank solution operators for forced linearized dynamics with arbitrarily time-dependent base flows. In particular, we use forced optimally time-dependent decomposition (f-OTD), which extracts the time-dependent correlated structures of the flow response to various excitations. Several demonstrations are included to illustrate the utility of the f-OTD low-rank approximation for performing global transient stability analysis. Additionally, we demonstrate the application of f-OTD in computing the post-transient response of linearized Navier-Stokes equations to a large number of impulses, which has applications in flow control.