Macroscopic modeling and simulations of room evacuation

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.