Modal Analysis and Sparse Identification Nonlinear Dynamics for Data-Driven Reduced Order Models of Shock-Separated Flows

Hypersonic systems are characterized by high-dimensional, nonlinear dynamical systems with structures across a large range of scales. Despite the apparent complexity of such flows, persistent behaviors are often determined by the balance of a few dominant physical processes that might be and the governing equations can be dramatically simplified. High fidelity numerical simulations of shock wave/turbulent boundary layer interactions (STBLIs) are analyzed via dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD) to uncover dynamically significant low-frequency modes. The results of each modal analysis are presented and the three-dimensional modal reconstructions for the DMD and SPOD are compared. The sparse identification of nonlinear dynamics (SINDy) algorithm is applied to the modal coefficients to develop low-order models for the low frequency dynamics present in the STBLIs. The SINDy models are compared to the numerical data, and we assess and discuss their performance.