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We consider a generalized version of the Hughes' macroscopic model of pedestrian motion. It consists of a conservation law on the pedestrian mass with an eikonal equation giving the direction of the flux depending of the density. The model displays a non-classical dynamics at the splitting point. Known convergence results for finite volume schemes do not apply in this setting. The wave- front tracking provides us with reference solutions to test numerically the convergence of classical finite volume schemes. These schemes will be used with a tracking algorithm to show the path of a single pedestrian during an evacuation. Resume. On considere une version generalisee du modele macroscopique de mouvements de foule de Hughes. Il se compose d'une loi de conservation sur la masse de pietons coupleeuneeikonale donnant la direction du flux selon la repartition des densitCe modele montre une dynamique non- classique au niveau du point de cesure. Les resultats de convergence pour les schemas aux volumes finis ne s'appliquent pas dans cette configuration. La methode de suivi des fronts fournit une solution de reference pour tester numeriquement la convergence de schemas classiques de volumes finis. Ces schemas seront utilises pour tracer la trajectoire d'un pieton uniquel'aide d'un algorithme additionnel.

Scalar conservation law with discontinuity arising in pedestrian modeling