Data-Driven Reduced Order Models

Abstract

In this chapter, we present the low-dimensional and data-driven analysis of unsteady fluid flow and fluid-structure interaction. Using the high-fidelity data from the full-order FSI model, we analyze the underlying dynamics using proper orthogonal decomposition (POD) techniques. The full-order data of flow past the square cylinder is decomposed into large-scale flow features using POD techniques. The energy cascade, nonlinearity capturing and reconstruction quality of the POD methods are examined. The low-dimensional projection of the data is used to explain the synchronization mechanism of the FSI system. This mechanism is further explored in the subcritical $$\mathrm{{Re}}$$ flows and moderately high $$\mathrm{{Re}}$$ turbulent flows as well. Unsteady flows involving fluid-structure interactions are widespread in numerous engineering applications and their fundamental understanding poses serious challenges due to the richness and complexity of nonlinear coupled physics. Even a simple configuration of a coupled fluid-structure system can exhibit complex spatial-temporal dynamics and synchronization as functions of physical parameters and geometric variations.