Modeling pedestrian flow via shallow water equations

We deal with the computer simulation of the movement of pedestrian crowds. A macroscopic model describing the pedestrian flow consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation, we get the first order hyperbolic system of partial differential equations with a source term. The splitting technique is applied which leads to a combination of the finite volume method for the hyperbolic problem with the numerical solution of the system of ordinary differential equations. Additionally, the solution of the so-called eikonal equation plays an important role here. Such a solution determines the density dependent direction of pedestrian motion. The algorithm giving the time evolution of the density and velocity of pedestrians in the two-dimensional domain is described. The practical application of the algorithm for the evacuationof the 2D hall for various configurations of obstacles near to the exit is presented.