کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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521544 | 867773 | 2013 | 21 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Computational Physics - Volume 237, 15 March 2013, Pages 299–319