Self-Organized Hydrodynamics with congestion and path formation in crowds

TL;DR

This paper introduces a continuum model for crowd dynamics incorporating alignment, repulsion, and congestion effects, along with a numerical scheme that effectively handles phase transitions and congestion phenomena.

Contribution

It presents a novel asymptotic-preserving numerical scheme for a hyperbolic system with singular pressure, enabling accurate simulation of congestion and path formation in crowds.

Findings

Efficient handling of congestion in numerical simulations.

Observation of phase transitions from compressible to incompressible flow.

Modeling of path formation in crowds using a two-fluid approach.

Abstract

A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the density and velocity orientation. Short-range repulsion is included through a singular pressure which becomes infinite at the jamming density. The singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics. The paper proposes an Asymptotic-Preserving scheme which takes care of the singular pressure while preventing the breakdown of the CFL stability condition near congestion. It relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation. Numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions. A two-fluid variant of the model provides a model of path formation in crowds.