A meshfree particle method for a vision-based macroscopic pedestrian model

Abstract

In this paper we present numerical simulations of a macroscopic vision-based model (Degond et al. in Kinet Relat Models AIMs 6(4):809–839, 2013) derived from microscopic situation rules described in Ondřej et al. (ACM Trans Graph 29(4):Article 123, 2010). This model describes an approach to collision avoidance between pedestrians by taking decisions of turning or slowing down based on basic interaction rules, where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle and of the time-to-interaction. A meshfree particle method is used to solve the equations of the model. Several numerical cases are considered to compare this model with models established in the field, for example, social force model coupled to an Eikonal equation (Etikyala et al. in Math Models Methods Appl Sci 20(12):2503–2523, 2014). Particular emphasis is put on the comparison of evacuation and computation times.