Two-Dimensional Approximate Godunov Scheme and What It Means For Continuum Pedestrian Flow Models

Abstract

An efficient simulation method for two-dimensional continuum pedestrian flow models is introduced. It is a two-dimensional adaptation of the Godunov scheme for one-dimensional road traffic flow models. It is further extended to include multiple classes, representing groups of pedestrians with different behavior, origin, and destination. The method can be applied to continuum pedestrian flow models in a wide range of applications from the design of train stations and other travel hubs to the study of crowd behavior and safety at sports, religious, and cultural events. The combination of the efficient simulation method with continuum models enables the user to get simulation results much quicker than before. This opens doors to real-time crowd control and to more advanced optimization of planning and control. Test results show the importance of choosing appropriate numerical settings, including grid cell and time step size for realistic simulation results.