On the numerical solutions of second order macroscopic models of pedestrian flows

The main target of this paper is focused on the numerical simulation of macroscopic models–two-dimensional hyperbolic conservation law - of pedestrian flows. Therefore, finite volume methods can be used to discretize the equations. Actually, the algorithms that have been used are particularly suited for solving hyperbolic problems. Moreover, simulations using first order accurate numerical solvers and first Godunov type schemes [S.K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mathematik Sbornik 47 (1959) 271–290] have been developed. This article is motivated by recent research activity focused on the problem of modelling systems of the living matter.