Macroscopic modeling and simulations of room evacuation

TL;DR

This paper compares two macroscopic crowd models, demonstrating the limitations of the Hughes model and showcasing the second order model's ability to simulate complex evacuation dynamics.

Contribution

It introduces a second order crowd model extending vehicular traffic models and applies advanced numerical methods to analyze evacuation scenarios.

Findings

Hughes' model cannot reproduce stop-and-go waves.

Second order model captures complex crowd behaviors.

Numerical simulations of room evacuation demonstrate model capabilities.

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.