Numerical Methods for Macroscopic Pedestrian Flow Models

In the study of crowd behaviour, most of the models consider only interaction among isolated individuals. However, a majority of the people in a crowd are moving in groups and social interactions can greatly influence crowd behaviour. It has been well recognized that a crowd is a mixture of individuals and groups rather than a pure collection of individuals. We propose a pedestrian flow model which includes the influence of group behaviours on crowd evacuation. We present a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an Eikonal equation. Hydrodynamic multi-group models are derived from the underlying particle system as well as scalar multi-group models. The Eikonal equation is used to compute optimal paths for the pedestrians. Meshfree particle methods are used to solve the equations on all levels of the hierarchy. Numerical test cases are investigated and the models and, in particular, the resulting evacuation times are compared for a wide range of parameters. As a general result we observe that the presence of pedestrian groups in the crowd increases the total crowd evacuation time. For calibration and validation of the proposed model, we compare our results with experimental data (Lu et al. in Transport Research Part C, 81: 317-329, 2017) of crowd evacuation in a university building. Simulation results are in good agreement with the experimental observations.