Scalar conservation law with discontinuity arising in pedestrian modeling

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