A numerical investigation of flux-limited approximations for pedestrian dynamics

A hierarchy of models for pedestrian flow with fixed speed is numerically investigated. The starting point is a microscopic model based on a stochastic interacting particle system coupled to an eikonal equation. Starting from this model a nonlocal and nonlinear flux-limited maximum-entropy equation for density and mean velocity is derived via a mean field kinetic equation. Finally, associated classical scalar equations for the density are considered for comparison. These models are compared to each other for different test cases showing the superiority of the flux-limited approach, in particular for situations with smaller values of the stochastic noise.