Numerical investigation of agent controlled pedestrian dynamics using a structure preserving finite volume scheme

TL;DR

This paper develops a structure-preserving finite volume numerical scheme for an optimal control model of pedestrian dynamics influenced by agents, applied to evacuation scenarios with simulations in various geometries.

Contribution

It introduces a novel finite volume scheme that maintains model constraints and applies it to agent-controlled pedestrian flow in evacuation scenarios.

Findings

Scheme preserves box constraints effectively

Numerical simulations demonstrate applicability to complex geometries

Model captures agent influence on pedestrian movement

Abstract

We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction.", arXiv 2011.03580, 2020. The model consists of a regularized variant of Hughes' model for pedestrian dynamics coupled to ordinary differential equations that describe the motion of agents which are able to influence the crowd via attractive forces. We devise a finite volume scheme that preserves the box constraints that are inherent in the model and discuss some of its properties. We apply our scheme to an objective functional tailored to the case of an evacuation scenario. Finally, numerical simulations for several practically relevant geometries are performed.