A viscous continuum model with smoke effect for pedestrian evacuation

A viscous continuum pedestrian flow model with smoke effect is presented to simulate pedestrian evacuation in a smoke-filled walking facility. The viscosity effect is taken into account to express pedestrians’ resistance to the velocity change. Pedestrians are presumed to be familiar with the walking environment and can temper their behavior to walk along a minimum-cost path. An Eikonal equation for the generalized walking cost is used to determine the navigation field of pedestrian motion. The generalized local walking cost includes the time of walking and other two costs caused by congestion and smoke avoiding behavior of pedestrians, respectively. The solution algorithm of the model in conservation-law form consists of a third-order WENO scheme for discretizing the convective terms, a fourth-order central scheme for discretizing the viscous terms and a second-order TVD Runge–Kutta scheme for time discretization. Numerical experiments are conducted to investigate macroscopic characteristics of pedestrian flow, pedestrian behavior characteristics and the factors influencing evacuation time in the presence of evolving smoke.