Non-local first-order modelling of crowd dynamics: a multidimensional framework with applications

Abstract

In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd-structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.

26 pages, 17 figures

References in corpus (5)

• Social Force Model for Pedestrian Dynamics
• The Dynamics of Crowd Disasters: An Empirical Study
• The Fundamental Diagram of Pedestrian Movement Revisited
• Time-evolving measures and macroscopic modeling of pedestrian flow
• Pedestrian flows in bounded domains with obstacles

Cited by in corpus (7)

• A hybrid mathematical model of collective motion under alignment and chemotaxis
• Viscous profiles in models of collective movements with negative diffusivities
• From individual behaviour to an evaluation of the collective evolution of crowds along footbridges
• Modeling micro-macro pedestrian counterflow in heterogeneous domains
• Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents
• Understanding Crowd Flow Movements Using Active-Langevin Model
• Semi-wavefront solutions in models of collective movements with density-dependent diffusivity