Macroscopic modeling and simulations of room evacuation
Abstract
We analyze numerically two macroscopic models of crowd
dynamics: the classical Hughes model and the second order model being
an extension to pedestrian motion of the Payne-Whitham vehicular
traffic model. The desired direction of motion is determined by solving
an eikonal equation with density dependent running cost, which results
in minimization of the travel time and avoidance of congested areas. We
apply a mixed finite volume-finite element method to solve the problems
and present error analysis for the eikonal solver, gradient computation
and the second order model yielding a first order convergence. We show
that Hughes’ model is incapable of reproducing complex crowd dynamics
such as stop-and-go waves and clogging at bottlenecks. Finally, using
the second order model, we study numerically the evacuation of pedestrians
from a room through a narrow exit.