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

Abstract

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.

Keywords:

• Crowd dynamics
• phase-transition
• continuum modelling
• numerical algorithm
• crowd turbulence

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work described in this paper was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Nos. 17201318 and 17204919) and the National Natural Science Foundation of China (Project No. 52302378). The first author was supported by the Shanghai Super Postdoctoral Incentive Program. The third author was supported by National Key R&D Program of China (Grant No. 2021YFA0719200). The fourth author was supported by NSF grant DMS-2010107. The last author was supported by the Francis S Y Bong Professorship in Engineering from the University of Hong Kong.