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

Abstract

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.