Network community-based model reduction for vortical flows

Abstract

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.

Network broadcast analysis and control of turbulent flows

“…10 1 10 2 10 3 10 -20 10 -15 10 -10 Gopalakrishnan Meena et al 2018;Murayama et al 2018). We treat each Cartesian element as a node in the network and the vortical interactions between the elements as the edges, as shown in figure 2(a).…”

“…2017; Scarsoglio, Cazzato & Ridolfi 2017). Network analysis has been used to study triadic interactions in turbulent flows (Gürcan 2017) and to model vortical interactions in Lagrangian and Eulerian settings (Nair & Taira 2015; Taira, Nair & Brunton 2016; Gopalakrishnan Meena, Nair & Taira 2018). Network-based frameworks have also been utilized to identify influential structures in complex flows using techniques such as spectral clustering (Hadjighasem et al.…”

“…Time series of fluid-flow properties have been considered to establish visibility graphs and recurrence networks, extracting dynamical features of complex flows (Godavarthi et al 2017;Scarsoglio, Cazzato & Ridolfi 2017). Network analysis has been used to study triadic interactions in turbulent flows (Gürcan 2017) and to model vortical interactions in Lagrangian and Eulerian settings (Nair & Taira 2015;Taira, Nair & Brunton 2016;Gopalakrishnan Meena, Nair & Taira 2018). Network-based frameworks have also been utilized to identify influential structures in complex flows using techniques such as spectral clustering (Hadjighasem et al 2016), coherent structure colouring (Schlueter-Kuck & Dabiri 2017), community detection (Murayama et al 2018;Gopalakrishnan Meena & Taira 2020) and graph comparison (Krueger et al 2019).…”

Sparsification of long range force networks for molecular dynamics simulations

“…Spectral sparsification used in this analysis requires all entries in the adjacency matrix to be positive. Incorporating both negative and positive charges into this formulation may be possible, but is beyond the scope of the current algorithm development [33]. Further research is required to understand how both positive and negative charges may be sparsified.…”

Crossroads of the mesoscale circulation

“…These methods are mainly devoted to the detection of barriers to transport in flow systems (Boffetta et al 2001;Abraham and Bowen 2002;d'Ovidio et al 2004;Beron-Vera et al 2008;Prants et al 2014a,b) or coherent regions (Lehahn et al 2007;Froyland et al 2007;d'Ovidio et al 2013;Berline et al 2014;Hadjighasem et al 2016;Miron et al 2017) with minimal leaking to surrounding water masses. Interestingly, during the last years, network theory approaches to geophysics (Phillips et al 2015), flow transport and mixing (Ser-Giacomi et al 2015a;Lindner and Donner 2017;Fujiwara et al 2017;Molkenthin et al 2017;Padberg-Gehle and Schneide 2017;Ser-Giacomi et al 2017;McAdam and van Sebille 2018), and turbulence (Iacobello et al 2018;Gopalakrishnan Meena et al 2018) have also attracted lot of interest.…”