Modeling and simulation of pedestrian flow through hydrodynamics

This paper proposes a pedestrian hydrodynamic model which takes a form for mass and "momentum" conservations with relaxation. The model can be viewed as an extension of the Aw-Rascle-Zhang vehicular traffic flow model, which ensures a so called "anisotropy" for traffic flow, namely, disturbance propagates only against the motion of the disturbed media. The optimal direction of motion for a pedestrian is determined by an Eikonal-type equation so that the total cost for traveling from the referred position to destination is minimized. A discontinuous Galerkin scheme is applied to solve the formulated hyperbolic system and the simulation indicates the convergence of the scheme. Moreover, numerical results demonstrate the ability of the model to depict macroscopic characteristics of pedestrian flow in normal situations, such as the formation and dissipation of congestion near the door in a walking facility. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Technology