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

TL;DR

This paper analyzes a hydrodynamic PDE model for swarming rigid bodies, establishing its hyperbolicity, non-conservativity, and deriving viscous corrections to aid numerical simulations.

Contribution

It demonstrates the hyperbolic nature of the model, introduces a conservative approximation via relaxation, and derives viscous corrections from kinetic limits.

Findings

The system is hyperbolic.

A conservative approximation is possible through relaxation.

Viscous corrections are derived from kinetic models.

Abstract

In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled 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.