Modelling crowd pressure and turbulence through a mixed-type continuum approach

Empirical studies of large gatherings and natural disasters have revealed two important features of dense crowds: extremely high crowd pressure and crowd turbulence. In this study, a mixed-type continuum model for multidirectional pedestrian flow was developed that explicitly considered the phase transition of different anticipation characteristics under different densities. Non-hyperbolicity was used to model the strong instabilities during crowd turbulence. In addition, by estimating the aggregated crowd pressure, the proposed model could clarify the effects of both force chains and panic sentiment, phenomena commonly observed during crowd disasters. The non-hyperbolic partial differential equations were solved using the mixed-type finite difference method, and Eikonal equations were solved using the fast sweeping method. Subsequently, the continuum model was applied to simulations of two real-world scenarios–the 2015 Hajj crowd disaster and the 2010 Love Parade crowd disaster–and validated through comparison with empirical observations. Overall, the proposed model is an efficient tool for evaluating crowd management strategies to predict and assess the crowd state.