A numerical investigation of pedestrian dynamics based on rational behaviour in different density scenarios

In this work, we extend a microscopic rational behaviour pedestrian model and investigate it and the related macroscopic model numerically. A coupling with an eikonal equation is performed to include more complex geometries and pedestrian behaviour. We compare the microscopic and macroscopic models to classical social force type models. We observe that the more complex rational behaviour approach gives physically more reasonable results in low-density cases. However, in higher density scenarios, an additional social force type term is required to avoid nonphysical overcrowding. We present numerical experiments and a numerical comparison with social force type models for a variety of different physical scenarios, including low and high density situations and flow problems with and without obstacles. The numerical simulations are realised by solving the model equations in a Lagrangian form using a mesh-free particle method. In this numerical context, the model is easily extended, for example, to moving obstacle scenarios, as presented in a final example.