The Lagrangian coordinate system and what it means for two-dimensional crowd flow models

TL;DR

This paper explores reformulating two-dimensional crowd flow models in the Lagrangian coordinate system, demonstrating potential computational advantages similar to those observed in one-dimensional traffic flow models.

Contribution

It extends the Lagrangian coordinate system approach from one-dimensional traffic to two-dimensional crowd flow modeling, showing initial promising results.

Findings

Lagrangian formulation is feasible for 2D crowd flow.

Initial simulations show computational benefits.

The approach opens new research directions.

Abstract

A continuum crowd flow model is reformulated in the Lagrangian coordinate system. The system has proven to give computational advantages over the traditional Eulerian coordinate system for (one-dimensional) road traffic flow. Our extension of the model and simulation method to (two-dimensional) crowd flow paves the way to explore whether the advantages also hold in two dimensions. This paper provides a first exploration and shows that a model and simulation method for two-dimensional crowd flow can be developed in the Lagrangian coordinate system and that is leads to promising results.