Communications in Mathematical Sciences

Volume 12 (2014)

Number 7

A Lagrangian approach for modeling road collisions using second-order models of traffic flow

Pages: 1239 – 1256



Salissou Moutari (CenSSOR, School of Mathematics and Physics, Queen’s University Belfast, United Kingdom)

Michael Herty (Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany)


In [M. Herty, A. Klein, S. Moutari, V. Schleper, and G. Steinaur, IMA J. Appl. Math., 78(5), 1087–1108, 2013] and [M. Herty and V. Schleper, ZAMM J. Appl. Math. Mech., 91, 763–776, 2011], a macroscopic approach, derived from fluid-dynamics models, has been introduced to infer traffic conditions prone to road traffic collisions along highways’ sections. In these studies, the governing equations are coupled within an Eulerian framework, which assumes fixed interfaces between the models. A coupling in Lagrangian coordinates would enable us to get rid of this (not very realistic) assumption. In this paper, we investigate the well-posedness and the suitability of the coupling of the governing equations within the Lagrangian framework. Further, we illustrate some features of the proposed approach through some numerical simulations.


road traffic collision, traffic flow, second-order model, Lagrangian formulation

2010 Mathematics Subject Classification


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