Self-organized hydrodynamics with congestion and path formation in crowds

Authors:
Pierre Degond;Jiale Hua
Affiliations:
Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France and CNRS, Institut de Mathématiques de Toulouse, UMR 5219, F-31062 Toulo ...;Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France and CNRS, Institut de Mathématiques de Toulouse, UMR 5219, F-31062 Toulo ...
Venue:
Journal of Computational Physics
Year:
2013

Citing 6
Cited 0

An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit

SIAM Journal on Numerical Analysis
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations

SIAM Journal on Scientific Computing
Resurrection of “second order” models of traffic flow

SIAM Journal on Applied Mathematics
Simulation of fluid and particles flows: Asymptotic preserving schemes for bubbling and flowing regimes

Journal of Computational Physics
Numerical simulations of the Euler system with congestion constraint

Journal of Computational Physics
An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

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 Courant-Friedrichs-Lewy (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.