Network community-based model reduction for vortical flows

A network community-based reduced-order model is developed to capture key interactions among coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

Figure 1

Overview of the community-based reduction of a networked dynamical system.

Figure 2

Lagrangian and Eulerian network descriptions of a flow field. Nodes (discrete point vortices and Cartesian cells) and edges (induced velocity $u$) of the vortical network in each descriptions are also shown.

Figure 3

Community-based networked dynamics of point vortices. The network structure and adjacency matrix at initial time ($t_0$), overall dynamics, and error between the community centroid dynamics for both the original dense ($n=100$) and the community-based reduced ($m=5$) point vortex systems are shown.

Figure 4

Network community-based reduction of the vortices in the von Kármán vortex street and force modeling.

Figure 5

Community-based reduced representation of a cylinder wake, and lift ($C_L$) and drag ($C_D$) forces on the cylinder predicted using the centroid-based reduced-order model. Resilience of the methodologies are tested using noisy flow field data.

Figure 6

Community-based reduced representation of a NACA 0012 airfoil wake classified under the 2P regime, and lift ($C_L$) and drag ($C_D$) forces on the airfoil predicted using the centroid-based reduced-order model. Resilience of the methodologies are tested using noisy flow field data.