Modeling and high-order numerical methods for pedestrian flow problems

In this talk, we would like to introduce a second-order mixed-type continuum model for multidirectional pedestrian flow problem that explicitly considers different movement characteristics of pedestrians under different situations. In addition to the phase transition, the proposed model can reveal the effects of both force chains and panic sentiment, which are commonly observed phenomena during crowd disasters, by estimating the aggregated pushing pressure. For solving these pedestrian flow models numerically, we apply high-order WENO and DG methods with positivity-preserving techniques. The continuum model was then applied to a real-world scenario, the 2010 Love Parade crowd disaster. Consistent with empirical observations, the simulation results revealed important features of the observed crowd, namely high density, high pressure, and crowd turbulence.