A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

TL;DR

This paper introduces a Semi-Lagrangian numerical scheme for a regularized Hughes model of pedestrian flow, incorporating small diffusion effects to better understand pedestrian exit dynamics.

Contribution

The paper develops and analyzes a Semi-Lagrangian scheme for a modified Hughes model with diffusion, providing insights into pedestrian flow and exit times.

Findings

Small diffusion influences pedestrian exit times

Numerical experiments demonstrate scheme stability and accuracy

Regularization improves model robustness

Abstract

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments.