Comparative analysis of model reduction techniques for flapping wing dynamics

Flows around flapping wings exhibit intricate vortex interactions and diverse dynamical regimes, requiring in-depth investigation to understand the underlying load generating mechanisms. Traditional computational fluid dynamics simulations are computationally demanding for long time resolution or even parametric exploration, prompting the adoption of reduced order models (ROMs) for efficiency. Model reduction techniques like proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and spectral proper orthogonal decomposition (SPOD) offer low-rank representations of high-dimensional flow-fields, crucial for constructing ROMs. However, applying these techniques to flows with moving boundaries, especially those generated using high-fidelity body non-conformal mesh-based methods like the immersed boundary method, is challenging. This study proposes a simple yet efficient approach to extend these different model reduction techniques to include moving solid boundaries in the flow-field, focusing on flapping wing problems. The suitability and shortcomings of the ROMs are analyzed on the basis of reconstruction error and their capability to obtain latent space representations that reflect the spatiotemporal scales of both periodic and aperiodic unsteady flows around a flapping airfoil at a low Reynolds number. Additionally, two recently proposed mode ranking strategies for DMD are compared and contrasted with the conventional method to improve its reconstruction capabilities, in the context of flapping wing dynamics. Overall, the results indicate that SPOD outperforms both POD and DMD in providing information-rich low-rank latent space and accurately reconstructing the flow-field across both periodic and aperiodic datasets.