New method for dynamic mode decomposition of flows over moving structures based on machine learning (hybrid dynamic mode decomposition)

Dynamic Mode Decomposition (DMD) is a data-driven reduced order method, which is known for its power to capture the basic features of dynamical systems. In fluid dynamics, modal analysis of unsteady fluid flows over moving structures is significant in terms of state estimation and control. However, the underlying algorithm of the DMD requires a fixed spatial domain, which is an obstacle for applying the DMD on the numerically investigated problems using dynamic meshes. In this study, a hybrid method called Hybrid Dynamic Mode Decomposition (HDMD) is presented for analysis of unsteady fluid flows over moving structures based on the DMD and machine learning. According to the assessment of several data interpolation methods, the K-nearest neighbor algorithm is employed for the interpolation of the numerical data from dynamic meshes at each time step to a single stationary grid. Three different case studies (rotating cylinder, oscillating airfoil, and Savonius wind turbine) are assessed to ensure the validity of the proposed method. Minimum mean R2 equal to 0.92 has been obtained for all of the mentioned cases, indicating the robustness of the HDMD algorithm for a variety of fluid flow simulations.