  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.
