Nonlinear Model-order Reduction for Oscillator Flows Using POD-DEIM

Model-order reduction techniques are key elements in the design and implementation of realistic flow control devices. In the past, efficient techniques have been developed for flows that can be described by their linearized dynamics. However, their efficiency has been limited when applied to flows that exhibit nonlinear behaviour — such as oscillator flows. In this article, we introduce a recently-developed technique for nonlinear model-order reduction based on multiple POD-bases and the discrete empirical interpolation method for oscillator-type flows. This technique is then demonstrated on the nonlinear Ginzburg–Landau equation, and applied to the compressible flow past a NACA-0012 aerofoil. It shows efficient and robust performance, while maintaining small residual error, and promises to be a valuable component in the flow analysis and the control design for nonlinear oscillator flows.