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Deep learning of vortex-induced vibrations

Published online by Cambridge University Press:  19 December 2018

Maziar Raissi Open the ORCID record for Maziar Raissi [Opens in a new window] ,
Zhicheng Wang Open the ORCID record for Zhicheng Wang [Opens in a new window] ,
Michael S. Triantafyllou Open the ORCID record for Michael S. Triantafyllou [Opens in a new window]  and
George Em Karniadakis
Maziar Raissi*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Zhicheng Wang
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Michael S. Triantafyllou
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
George Em Karniadakis
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: [email protected]
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Abstract

Vortex-induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not straightforward to solve using standard computational fluid dynamics methods, especially since no information is provided for the pressure. An even greater challenge is to infer the lift and drag forces given some dye or smoke visualizations of the flow field. Here we employ deep neural networks that are extended to encode the incompressible Navier–Stokes equations coupled with the structure’s dynamic motion equation. In the first case, given scattered data in space–time on the velocity field and the structure’s motion, we use four coupled deep neural networks to infer very accurately the structural parameters, the entire time-dependent pressure field (with no prior training data), and reconstruct the velocity vector field and the structure’s dynamic motion. In the second case, given scattered data in space–time on a concentration field only, we use five coupled deep neural networks to infer very accurately the vector velocity field and all other quantities of interest as before. This new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.

JFM classification

Mathematical Foundations: Computational methods Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 119 - 137
Copyright
© 2018 Cambridge University Press 

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