Trajectory-optimized cluster-based network model for the three-dimensional sphere wake

We propose a fully automatable data-driven method to model unsteady flow dynamics, namely the trajectory-optimized Cluster-based Network Model (tCNM). Stating with CNM [1,2], the snapshot trajectories are tracked with improved accuracy by tCNM, where centroids are shifted to obtain a more accurate representation, and supporting points are added to get a refined state propagation. Three-dimensional sphere wakes are used to validate tCNM, including periodic shedding, quasi-periodic shedding and chaotic shedding. The representation error is five times smaller compared to the closest centroid approximation. This improvement indicates that tCNM can achieve the same accuracy as Proper Orthogonal Decomposition (POD) of the same order, while retaining the advantage of high physical interpretability. tCNM and other extensions of cluster-based modeling [3,4] constitute a promising alternative to POD methods, which can be applied to numerous other applications and extended to parametric and control-oriented reduced-order models.