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.

本文提出了一种二阶行人模型，该模型包含两种类型的方程：连续性方程和运输方程组。为了完善模型，我们开发了Eikonal方程来明确考虑个人的集体决策和人群压力对行人动态的影响。然后，在适当的初始和边界条件下，使用一组偏微分方程组模拟人群运动。基于通过执行标准线性稳定性分析得出的稳定性要求，选择合适的参数以在数值示例中测试模型。然后，使用特征方式的三阶加权基本非振荡（WENO3）方案求解所提出的二阶系统，并使用快速扫描方法求解Eikonal方程。数值结果表明了该模型的有效性，因为导出的局部流量密度关系在高密度区域中产生了第二个峰值，这与以前的经验研究是一致的。此外，通过对诸如停停走走波等复杂现象的仿真，验证了该模型在不稳定条件下的适用性。此外，模拟结果中人群压力的估计值可以用作人群管理和控制的风险级别指标。