A Continuum model for pedestrian flow with explicit consideration of crowd force and panic effects

• Published in: Transportation research. Part B: methodological 2021-07, Vol.149, p.100-117
• Main Authors: Liang, Haoyang, Du, Jie, Wong, S.C.
• Format: Article
• Language: English
• Subjects: Boundary conditions; Continuity equation; Continuum modeling; Crowd force; Density; Differential equations; Empirical analysis; Higher-order traffic model; Level indicators; Local flow; Mathematical models; Model testing; Numerical solution; Partial differential equations; Pedestrian flow; Pedestrian traffic flow; Risk levels; Risk management; Simulation; Stability analysis; Transport equations
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2021.05.006

•Formulation of a higher-order macroscopic model for pedestrian movements with explicit consideration of panic sentiment and pushing force.•Development of efficient solution algorithms.•Analytical analysis and numerical simulation of unstable phenomena at certain conditions.•Critical analysis of the effects of the crowd pressure on pedestrian dynamics. This paper proposes a second-order pedestrian model that comprises two types of equations: continuity equation and a set of transport equations. To complete the model, we develop Eikonal equations to explicitly consider the effects of the collective decisions of individuals and crowd pressure on pedestrian dynamics. Then, the crowd movement is simulated using a set of partial differential equations under appropriate initial and boundary conditions. Based on the stability requirements derived by performing a standard linear stability analysis, suitable parameters are selected to test the model in a numerical example. The proposed second-order system is then solved using the characteristic-wise third-order weighted essentially non-oscillatory (WENO3) scheme, and the Eikonal equations are solved using the fast sweeping method. The numerical results indicate the effectiveness of the model because the derived local flow-density relationship produces a second peak in the high-density region, which is consistent with previous empirical studies. Besides, the applicability of the model to an unstable condition is verified through the simulation of complex phenomena such as stop-and-go waves. Furthermore, the estimate of crowd pressure in the simulation results can be used as a risk-level indicator for crowd management and control.