Self-organized hydrodynamics with congestion and path formation in crowds

JOURNAL OF COMPUTATIONAL PHYSICS

卷:237

Article

Degond, Pierre¹ 

[1] Univ Toulouse, UPS, Inst Math Toulouse, INSA,UT1,UTM, F-31062 Toulouse, France

关键词: Self-propelled particles;    Oientation dynamics;    Self-organization;    Hydrodynamic limit;    Volume exclusion;    Congestion;    Jamming;    Finite volumes;    Asymptotic-Preserving scheme;    Herds;    Crowds;    Path formation;   

DOI  :  10.1016/j.jcp.2012.11.033

来源: Elsevier

【 摘 要 】

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. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free