Modeling pedestrian flow through a bottleneck based on a second-order continuum model

Abstract

Large numbers of pedestrians moving in a two-dimensional continuous walking facility can be regarded as a continuum fluid that is governed by the conservation laws of fluid dynamics. Pedestrian flow differs from common flows driven by a pressure difference in that it has special path-choice behaviors associated with the purpose of the trip. This paper presents a new second-order continuum model for pedestrian flow to study the collective behaviors of a large-scale crowd in front of a bottleneck that are important for the planning and design of walking facilities. A pressure term is introduced to describe how pedestrians react to the state of traffic in the desired direction of motion of pedestrian flow. The desired direction of motion is determined by an Eikonal equation on the instantaneous walking cost caused by pedestrians walking to the final destination in a reactive manner. The solution algorithm is composed of a third-order fast sweeping method for the Eikonal equation and a third-order WENO method for the continuum model in a conservation-law form. Numerical experiments of pedestrian flow passing through a bottleneck of varying widths are carried out to verify the proposed model and algorithm.