Macroscopic modeling and simulations of room evacuation

Abstract

International audienceWe analyze numerically two macroscopic models of crowddynamics: the classical Hughes model and the second order model beingan extension to pedestrian motion of the Payne-Whitham vehiculartraffic model. The desired direction of motion is determined by solvingan eikonal equation with density dependent running cost, which resultsin minimization of the travel time and avoidance of congested areas. Weapply a mixed finite volume-finite element method to solve the problemsand present error analysis for the eikonal solver, gradient computationand the second order model yielding a first order convergence. We showthat Hughes’ model is incapable of reproducing complex crowd dynamicssuch as stop-and-go waves and clogging at bottlenecks. Finally, usingthe second order model, we study numerically the evacuation of pedestriansfrom a room through a narrow exit