The Hughes model for pedestrian dynamics and congestion modelling

TL;DR

This paper numerically investigates variations of the Hughes model for pedestrian flow, focusing on congestion effects, by developing an efficient semi-Lagrangian scheme to analyze how different congestion penalizations influence crowd dynamics.

Contribution

It introduces a semi-Lagrangian numerical scheme for the Hughes model and explores the impact of various congestion penalizations on pedestrian flow.

Findings

The scheme effectively approximates solutions of the coupled PDE system.

Different penalization functions significantly affect congestion patterns.

The model provides insights into crowd movement under various congestion scenarios.

Abstract

In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation and a first order conservation law, and it intends to approximate the flow of a large pedestrian group aiming to reach a target as fast as possible, while taking into account the congestion of the crowd. We propose an efficient semi-Lagrangian scheme (SL) to approximate the solution of the PDE system and we investigate the macroscopic effects of different penalization functions modelling the congestion phenomena.