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Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies

Degond, Pierre; Frouvelle, Amic; Merino Aceituno, Sara; Trescases, Ariane (2022), Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies, Quarterly of Applied Mathematics, p. 34

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Type
Article accepté pour publication ou publié
External document link
https://hal.science/hal-03833710
Date
2022
Journal name
Quarterly of Applied Mathematics
Publisher
American Mathematical Society
Pages
34
Metadata
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Author(s)
Degond, Pierre
Frouvelle, Amic
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Merino Aceituno, Sara
Trescases, Ariane
Abstract (EN)
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting selfpropelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.
Subjects / Keywords
Self-organized hydrodynamics; Vicsek model; relaxation approximation; viscosity; invariances; dimension reduction