The Hughes model for pedestrian dynamics and congestion modelling
  In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation and a first order conservation law, and it intends to approximate the flow of a large pedestrian group aiming to reach a target as fast as possible, while taking into account the congestion of the crowd.   We propose an efficient semi-Lagrangian scheme (SL) to approximate the solution of the PDE system and we investigate the macroscopic effects of different penalization functions modelling the congestion phenomena. 
Elisabetta Carlini, Adriano Festa and Francisco J. Silva
math.NA