Ludovic Leclercq

Titre : The LWR model in Lagrangian coordinates


Recent developments in traffic flow theory have led to efficient numerical schemes for solving macroscopic models. They are obtained by solving the models in Lagrangian rather than the traditional Eulerian coordinates. Additionally, variational theory and its extension in the Lagrangian framework make it possible to prove that these schemes are exact for first order models when the fundamental diagram is triangular.

The aim of this presentation is to present the Lagrangian formulation of the LWR (first order) model and its extension to multiple vehicle types. Variational theory will be used for deriving efficient numerical schemes that are exact under few restrictive assumptions.